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3.0

Jun 29, 2018
06/18

by
Cristina Butucea; Rania Zgheib

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We observe $n$ independent $p-$dimensional Gaussian vectors with missing coordinates, that is each value (which is assumed standardized) is observed with probability $a>0$. We investigate the problem of minimax nonparametric testing that the high-dimensional covariance matrix $\Sigma$ of the underlying Gaussian distribution is the identity matrix, using these partially observed vectors. Here, $n$ and $p$ tend to infinity and $a>0$ tends to 0, asymptotically. We assume that $\Sigma$...

Topics: Statistics, Statistics Theory, Mathematics

Source: http://arxiv.org/abs/1602.04310

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11

Jun 27, 2018
06/18

by
Christopher Ferrie; Robin Blume-Kohout

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A minimax estimator has the minimum possible error ("risk") in the worst case. We construct the first minimax estimators for quantum state tomography with relative entropy risk. The minimax risk of non-adaptive tomography scales as $O(1/\sqrt{N})$, in contrast to that of classical probability estimation which is $O(1/N)$. We trace this deficiency to sampling mismatch: future observations that determine risk may come from a different sample space than the past data that determine the...

Topics: Quantum Physics, Statistics, Mathematics, Statistics Theory

Source: http://arxiv.org/abs/1503.03100

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8.0

Jun 27, 2018
06/18

by
Siva Sivaganesan

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Discussion of Overall Objective Priors by James O. Berger, Jose M. Bernardo, Dongchu Sun [arXiv:1504.02689].

Topics: Statistics, Mathematics, Statistics Theory

Source: http://arxiv.org/abs/1504.07046

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4.0

Jun 29, 2018
06/18

by
Xiaohong Chen; Timothy Christensen; Keith O'Hara; Elie Tamer

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In complicated/nonlinear parametric models, it is generally hard to determine whether the model parameters are (globally) point identified. We provide computationally attractive procedures to construct confidence sets (CSs) for identified sets of parameters in econometric models defined through a likelihood or a vector of moments. The CSs for the identified set or for a function of the identified set (such as a subvector) are based on inverting an optimal sample criterion (such as likelihood or...

Topics: Mathematics, Methodology, Statistics Theory, Statistics

Source: http://arxiv.org/abs/1605.00499

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5.0

Jun 30, 2018
06/18

by
Markus Reiß; Leonie Selk

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For nonparametric regression with one-sided errors and a boundary curve model for Poisson point processes we consider the problem of efficient estimation for linear functionals. The minimax optimal rate is obtained by an unbiased estimation method which nevertheless depends on a H\"older condition or monotonicity assumption for the underlying regression or boundary function. We first construct a simple blockwise estimator and then build up a nonparametric maximum-likelihood approach for...

Topics: Mathematics, Statistics Theory, Statistics

Source: http://arxiv.org/abs/1407.4229

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5.0

Jun 29, 2018
06/18

by
Rana Fakhereddine; Rami El Haddad; Christian Lécot

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We present several Monte Carlo strategies for simulating discrete-time Markov chains with continuous multi-dimensional state space; we focus on stratified techniques. We first analyze the variance of the calculation of the measure of a domain included in the unit hypercube, when stratified samples are used. We then show that each step of the simulation of a Markov chain can be reduced to the numerical integration of the indicator function of a subdomain of the unit hypercube. Our approach for...

Topics: Statistics, Statistics Theory, Mathematics

Source: http://arxiv.org/abs/1603.06386

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3.0

Jun 29, 2018
06/18

by
Andee Kaplan; Daniel Nordman; Stephen Vardeman

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A probability model exhibits instability if small changes in a data outcome result in large, and often unanticipated, changes in probability. For correlated data structures found in several application areas, there is increasing interest in predicting/identifying instability. We consider the problem of quantifying instability for general probability models defined on sequences of observations, where each sequence of length N has a finite number of possible outcomes. (A sequence of probability...

Topics: Statistics, Statistics Theory, Mathematics

Source: http://arxiv.org/abs/1612.01159

3
3.0

Jun 30, 2018
06/18

by
Igor Vladimirovich Rodionov

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The goodness-of-fit test for discrimination of two tail distribution using higher order statistics is proposed. The consistency of proposed test is proved for two different alternatives. We do not assume belonging the corresponding distribution function to a maximum domain of attraction.

Topics: Statistics Theory, Statistics, Mathematics

Source: http://arxiv.org/abs/1702.05641

3
3.0

Jun 29, 2018
06/18

by
Shuyang Bai; Murad S. Taqqu

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Mathematically, under long memory, one can obtain so-called non-central limit theorems involving non-Gaussian limits. In these non-central limit theorems, a positive integer called "Hermite rank" plays a crucial role. The non-Gaussian limit appears only when the Hermite rank is greater than one. From a practical point of view, however, we argue that an Hermite rank greater than one is unstable. In contrast, an Hermite rank equal to one is stable. We provide empirical evidence...

Topics: Statistics, Statistics Theory, Mathematics

Source: http://arxiv.org/abs/1610.00690

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8.0

Jun 26, 2018
06/18

by
Luiz A. Baccalá; Daniel Y. Takahashi; Koichi Sameshima

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We present a unified mathematical derivation of the asymptotic behaviour of three of the main forms of \textit{directed transfer function} (DTF) complementing recent partial directed coherence (PDC) results \cite{Baccala2013}. Based on these results and numerical examples we argue for a new directed `link' centered neural connectivity framework to replace the widespread correlation based effective/functional network concepts so that directed network influences between structures become...

Topics: Neurons and Cognition, Quantitative Biology, Mathematics, Statistics Theory, Statistics

Source: http://arxiv.org/abs/1501.05836

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4.0

Jun 30, 2018
06/18

by
Peter Binev; Albert Cohen; Wolfgang Dahmen; Ronald DeVore

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Algorithms for binary classification based on adaptive tree partitioning are formulated and analyzed for both their risk performance and their friendliness to numerical implementation. The algorithms can be viewed as generating a set approximation to the Bayes set and thus fall into the general category of set estimators. In contrast with the most studied tree-based algorithms, which utilize piecewise constant approximation on the generated partition [IEEE Trans. Inform. Theory 52 (2006)...

Topics: Mathematics, Statistics Theory, Statistics

Source: http://arxiv.org/abs/1411.0839

3
3.0

Jun 30, 2018
06/18

by
Jirô Akahori; Nien-Lin Liu; Maria Elvira Mancino; Yukie Yasuda

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In this paper we present a slight modification of the Fourier estimation method of the spot volatility (matrix) process of a continuous It\^o semimartingale where the estimators are always non-negative definite. Since the estimators are factorized, computational cost will be saved a lot.

Topics: Mathematics, Quantitative Finance, Statistical Finance, Statistics Theory, Statistics

Source: http://arxiv.org/abs/1410.0112

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2.0

Jun 30, 2018
06/18

by
Jean Jacod; Viktor Todorov

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We propose new nonparametric estimators of the integrated volatility of an It\^{o} semimartingale observed at discrete times on a fixed time interval with mesh of the observation grid shrinking to zero. The proposed estimators achieve the optimal rate and variance of estimating integrated volatility even in the presence of infinite variation jumps when the latter are stochastic integrals with respect to locally "stable" L\'{e}vy processes, that is, processes whose L\'{e}vy measure...

Topics: Mathematics, Statistics Theory, Statistics

Source: http://arxiv.org/abs/1405.7483

2
2.0

Jun 30, 2018
06/18

by
Viktor Witkovský; Gejza Wimmer; Tomy Duby

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We introduce a class of logarithmic Lambert W random variables for a specific family of distributions. In particular, we characterize the log-Lambert W random variables for chi-squared distributions which naturally appear in the likelihood based inference of normal random variables.

Topics: Mathematics, Statistics Theory, Statistics

Source: http://arxiv.org/abs/1406.0345

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3.0

Jun 30, 2018
06/18

by
Walter Dempsey; Peter McCullagh

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Pilgrim's monopoly is a probabilistic process giving rise to a non-negative sequence $T_1, T_2,\ldots$ that is infinitely exchangeable, a natural model for time-to-event data. The one-dimensional marginal distributions are exponential. The rules are simple, the process is easy to generate sequentially, and a simple expression is available for both the joint density and the multivariate survivor function. There is a close connection with the Kaplan-Meier estimator of the survival distribution....

Topics: Mathematics, Statistics Theory, Statistics

Source: http://arxiv.org/abs/1412.1490

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6.0

Jun 30, 2018
06/18

by
Sören R. Künzel; David Pollard; Dana Yang

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We were trying to understand the analysis provided by Kneip (1994, Ordered Linear Smoothers). In particular we wanted to persuade ourselves that his results imply the oracle inequality stated by Tsybakov (2014, Lecture 8). This note contains our reworking of Kneip's ideas.

Topics: Mathematics, Statistics Theory, Statistics

Source: http://arxiv.org/abs/1405.1744

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2.0

Jun 30, 2018
06/18

by
Jay Bartroff

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The $\gamma$-FDP and $k$-FWER multiple testing error metrics, which are tail probabilities of the respective error statistics, have become popular recently as less-stringent alternatives to the FDR and FWER. We propose general and flexible stepup and stepdown procedures for testing multiple hypotheses about sequential (or streaming) data that simultaneously control both the type I and II versions of $\gamma$-FDP, or $k$-FWER. The error control holds regardless of the dependence between data...

Topics: Mathematics, Statistics, Statistics Theory, Methodology

Source: http://arxiv.org/abs/1406.5933

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2.0

Jun 30, 2018
06/18

by
Tobias Kley; Stanislav Volgushev; Holger Dette; Marc Hallin

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Quantile- and copula-related spectral concepts recently have been considered by various authors. Those spectra, in their most general form, provide a full characterization of the copulas associated with the pairs $(X_t,X_{t-k})$ in a process $(X_t)_{t\in\mathbb{Z}}$, and account for important dynamic features, such as changes in the conditional shape (skewness, kurtosis), time-irreversibility, or dependence in the extremes that their traditional counterparts cannot capture. Despite various...

Topics: Mathematics, Statistics Theory, Statistics

Source: http://arxiv.org/abs/1401.8104

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3.0

Jun 30, 2018
06/18

by
Anne Marie Svane

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It has been shown that local algorithms based on grey-scale images sometimes lead to asymptotically unbiased estimators for surface area and integrated mean curvature. This paper extends the results to estimators for Minkowski tensors. In particular, asymptotically unbiased local algorithms for estimation of all volume and surface tensors and certain mean curvature tensors are given. This requires an extension of the known asymptotic formulas to estimators with position dependent weights.

Topics: Mathematics, Statistics Theory, Statistics

Source: http://arxiv.org/abs/1401.7790

2
2.0

Jun 30, 2018
06/18

by
Junhyong Kim; Elchanan Mossel; Miklós Z. Rácz; Nathan Ross

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Reconstructing past population size from present day genetic data is a major goal of population genetics. Recent empirical studies infer population size history using coalescent-based models applied to a small number of individuals. Here we provide tight bounds on the amount of exact coalescence time data needed to recover the population size history of a single, panmictic population at a certain level of accuracy. In practice, coalescence times are estimated from sequence data and so our lower...

Topics: Populations and Evolution, Mathematics, Quantitative Biology, Statistics Theory, Statistics

Source: http://arxiv.org/abs/1402.2424

2
2.0

Jun 30, 2018
06/18

by
Anna Ben-Hamou; Stéphane Boucheron; Mesrob I. Ohannessian

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An infinite urn scheme is defined by a probability mass function $(p_j)_{j\geq1}$ over positive integers. A random allocation consists of a sample of $N$ independent drawings according to this probability distribution where $N$ may be deterministic or Poisson-distributed. This paper is concerned with occupancy counts, that is with the number of symbols with $r$ or at least $r$ occurrences in the sample, and with the missing mass that is the total probability of all symbols that do not occur in...

Topics: Mathematics, Statistics Theory, Statistics

Source: http://arxiv.org/abs/1412.8652

2
2.0

Jun 30, 2018
06/18

by
Marek Arendarczyk; Krzysztof Dȩbicki; Michel Mandjes

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In this paper, the area swept under the workload graph is analyzed: with $\{Q(t) : t\ge0\}$ denoting the stationary workload process, the asymptotic behavior of \[\pi_{T(u)}(u):={\mathbb{P}}\biggl(\int_0^ {T(u)}Q(r)\,\mathrm{d}r>u\biggr)\] is analyzed. Focusing on regulated Brownian motion, first the exact asymptotics of $\pi_{T(u)}(u)$ are given for the case that $T(u)$ grows slower than $\sqrt{u}$, and then logarithmic asymptotics for (i) $T(u)=T\sqrt{u}$ (relying on sample-path large...

Topics: Mathematics, Statistics Theory, Statistics

Source: http://arxiv.org/abs/1403.1665

3
3.0

Jun 30, 2018
06/18

by
Xin Jiang; Garvesh Raskutti; Rebecca Willett

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This paper considers fundamental limits for solving sparse inverse problems in the presence of Poisson noise with physical constraints. Such problems arise in a variety of applications, including photon-limited imaging systems based on compressed sensing. Most prior theoretical results in compressed sensing and related inverse problems apply to idealized settings where the noise is i.i.d., and do not account for signal-dependent noise and physical sensing constraints. Prior results on Poisson...

Topics: Mathematics, Statistics Theory, Statistics

Source: http://arxiv.org/abs/1403.6532

3
3.0

Jun 30, 2018
06/18

by
Zoltan Szabo

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We present ITE (information theoretical estimators) a free and open source, multi-platform, Matlab/Octave toolbox that is capable of estimating many different variants of entropy, mutual information, divergence, association measures, cross quantities, and kernels on distributions. Thanks to its highly modular design, ITE supports additionally (i) the combinations of the estimation techniques, (ii) the easy construction and embedding of novel information theoretical estimators, and (iii) their...

Topics: Statistics, Mathematics, Computing Research Repository, Information Theory, Statistics Theory,...

Source: http://arxiv.org/abs/1405.2106

3
3.0

Jun 29, 2018
06/18

by
M Ahmed; V Maume-Deschamps; P Ribereau; Céline Vial

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In this paper, we study the quantitative behavior of a spatial risk measure corresponding to a damage function and a region, taking into account the spatial dependence of the underlying process. This kind of risk measure has already been introduced and studied for some max-stable processes in [Koch2015]. In this paper, we consider isotropic Gaussian processes and the excess damage function over a threshold. We performed a simulation study and a real data study.

Topics: Statistics, Probability, Statistics Theory, Mathematics

Source: http://arxiv.org/abs/1612.08280

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6.0

Jun 30, 2018
06/18

by
Wilfrid S. Kendall

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The use of barycentres in data analysis is illustrated, using as example a dataset of hurricane trajectories.

Topics: Mathematics, Statistics Theory, Statistics

Source: http://arxiv.org/abs/1406.7173

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9.0

Jun 30, 2018
06/18

by
Evgeny Spodarev; Peter Straka; Steffen Winter

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Most of the known methods for estimating the fractal dimension of fractal sets are based on the evaluation of a single geometric characteristic, e.g. the volume of its parallel sets. We propose a method involving the evaluation of several geometric characteristics, namely all the intrinsic volumes (i.e.\ volume, surface area, Euler characteristic etc.) of the parallel sets of a fractal. Motivated by recent results on their limiting behaviour, we use these functionals to estimate the fractal...

Topics: Mathematics, Metric Geometry, Statistics Theory, Statistics

Source: http://arxiv.org/abs/1408.6333

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2.0

Jun 30, 2018
06/18

by
A. Philip Dawid; Monica Musio

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Bayesian model selection with improper priors is not well-defined because of the dependence of the marginal likelihood on the arbitrary scaling constants of the within-model prior densities. We show how this problem can be evaded by replacing marginal log-likelihood by a homogeneous proper scoring rule, which is insensitive to the scaling constants. Suitably applied, this will typically enable consistent selection of the true model.

Topics: Mathematics, Statistics Theory, Statistics

Source: http://arxiv.org/abs/1409.5291

3
3.0

Jun 30, 2018
06/18

by
Mark K. Transtrum; Gus Hart; Peng Qiu

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We develop a language for describing the relationship among observations, mathematical models, and the underlying principles from which they are derived. Using Information Geometry, we consider geometric properties of statistical models for different observations. As observations are varied, the model manifold may be stretched, compressed, or even collapsed. Observations that preserve the structural identifiability of the parameters also preserve certain topological features (such as edges and...

Topics: Physics, Data Analysis, Statistics and Probability, Statistics, Mathematics, Statistics Theory,...

Source: http://arxiv.org/abs/1409.6203

2
2.0

Jun 30, 2018
06/18

by
Vladimir Spokoiny; Mayya Zhilova

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A multiplier bootstrap procedure for construction of likelihood-based confidence sets is considered for finite samples and a possible model misspecification. Theoretical results justify the bootstrap validity for a small or moderate sample size and allow to control the impact of the parameter dimension $p$: the bootstrap approximation works if $p^3/n$ is small. The main result about bootstrap validity continues to apply even if the underlying parametric model is misspecified under the so-called...

Topics: Mathematics, Statistics Theory, Statistics

Source: http://arxiv.org/abs/1410.0347

2
2.0

Jun 30, 2018
06/18

by
Xiaohong Chen; Demian Pouzo

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This paper considers inference on functionals of semi/nonparametric conditional moment restrictions with possibly nonsmooth generalized residuals, which include all of the (nonlinear) nonparametric instrumental variables (IV) as special cases. These models are often ill-posed and hence it is difficult to verify whether a (possibly nonlinear) functional is root-$n$ estimable or not. We provide computationally simple, unified inference procedures that are asymptotically valid regardless of...

Topics: Mathematics, Statistics Theory, Statistics

Source: http://arxiv.org/abs/1411.1144

2
2.0

Jun 30, 2018
06/18

by
Marianna Pensky

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The present paper considers a problem of estimating a linear functional $\Phi=\int_{-\infty}^\infty \varphi(x) f(x)dx$ of an unknown deconvolution density $f$ on the basis of i.i.d. observations $Y_i = \theta_i + \xi_i$ where $\xi_i$ has a known pdf $g$ and $f$ is the pdf of $\theta_i$. Although various aspects and particular cases of this problem have been treated by a number of authors, there are still many gaps. In particular, there are no minimax lower bounds for an estimator of $\Phi$ for...

Topics: Mathematics, Statistics Theory, Statistics

Source: http://arxiv.org/abs/1411.1660

2
2.0

Jun 30, 2018
06/18

by
Johannes Dueck; Dominic Edelmann; Donald Richards

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We generalize an integral which arises in several areas in probability and statistics and which is at the core of the field of distance correlation, a concept developed by Sz\'ekely, Rizzo and Bakirov (2007) to measure dependence between random variables. Let $m$ be a positive integer and let ${\cos_m}(u)$, $u \in \mathbb{R}$, be the truncated Maclaurin expansion of ${\cos}(u)$, where the expansion is truncated at the $m$th summand. For $t, x \in \mathbb{R}^d$, let $\langle t,x\rangle$ and...

Topics: Mathematics, Statistics Theory, Statistics

Source: http://arxiv.org/abs/1411.1312

3
3.0

Jun 30, 2018
06/18

by
Azzouz Dermoune; Aziz El Kaabouchi

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The data $(y_i,x_i)\in$ $\textbf{R}\times[a,b]$, $i=1,\ldots,n$ satisfy $y_i=s(x_i)+e_i$ where $s$ belongs to the set of cubic splines. The unknown noises $(e_i)$ are such that $var(e_I)=1$ for some $I\in \{1, \ldots, n\}$ and $var(e_i)=\sigma^2$ for $i\neq I$. We suppose that the most important noise is $e_I$, i.e. the ratio $r_I=\frac{1}{\sigma^2}$ is larger than one. If the ratio $r_I$ is large, then we show, for all smoothing parameter, that the penalized least squares estimator of the...

Topics: Mathematics, Statistics Theory, Statistics

Source: http://arxiv.org/abs/1406.1629

2
2.0

Jun 30, 2018
06/18

by
James E. Barrett; Anthony C. C. Coolen

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The analysis of high dimensional survival data is challenging, primarily due to the problem of overfitting which occurs when spurious relationships are inferred from data that subsequently fail to exist in test data. Here we propose a novel method of extracting a low dimensional representation of covariates in survival data by combining the popular Gaussian Process Latent Variable Model (GPLVM) with a Weibull Proportional Hazards Model (WPHM). The combined model offers a flexible non-linear...

Topics: Mathematics, Statistics Theory, Statistics, Methodology

Source: http://arxiv.org/abs/1406.0812

2
2.0

Jun 30, 2018
06/18

by
Takumi Saegusa

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We propose a nonparametric bootstrap procedure for two-phase stratified sampling without replacement. In this design, a weighted likelihood estimator is known to have smaller asymptotic variance than under the convenient assumption of independence often made in practice. Variance estimation, however, has not been well studied for semiparametric models where variance may not have a closed form. Motivated by semiparametric inference, we establish conditional weak convergence of bootstrap inverse...

Topics: Mathematics, Statistics Theory, Statistics

Source: http://arxiv.org/abs/1406.5580

2
2.0

Jun 30, 2018
06/18

by
Valentine Genon-Catalot; Catherine Larédo

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We prove a global asymptotic equivalence of experiments in the sense of Le Cam's theory. The experiments are a continuously observed diffusion with nonparametric drift and its Euler scheme. We focus on diffusions with nonconstant-known diffusion coefficient. The asymptotic equivalence is proved by constructing explicit equivalence mappings based on random time changes. The equivalence of the discretized observation of the diffusion and the corresponding Euler scheme experiment is then derived....

Topics: Mathematics, Statistics Theory, Statistics

Source: http://arxiv.org/abs/1406.5863

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2.0

Jun 30, 2018
06/18

by
Samuel Maistre; Valentin Patilea

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Regression models with a response variable taking values in a Hilbert space and hybrid covariates are considered. This means two sets of regressors are allowed, one of finite dimension and a second one functional with values in a Hilbert space. The problem we address is the test of the effect of the functional covariates. This problem occurs for instance when checking the goodness-of-fit of some regression models for functional data. The significance test for functional regressors in...

Topics: Mathematics, Statistics Theory, Statistics

Source: http://arxiv.org/abs/1406.6227

2
2.0

Jun 30, 2018
06/18

by
Andreas Hagemann

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In this paper I develop a wild bootstrap procedure for cluster-robust inference in linear quantile regression models. I show that the bootstrap leads to asymptotically valid inference on the entire quantile regression process in a setting with a large number of small, heterogeneous clusters and provides consistent estimates of the asymptotic covariance function of that process. The proposed bootstrap procedure is easy to implement and performs well even when the number of clusters is much...

Topics: Mathematics, Statistics Theory, Statistics

Source: http://arxiv.org/abs/1407.7166

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2.0

Jun 30, 2018
06/18

by
Zhigang Bao; Jiang Hu; Guangming Pan; Wang Zhou

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Consider a normal vector $\mathbf{z}=(\mathbf{x}',\mathbf{y}')'$, consisting of two sub-vectors $\mathbf{x}$ and $\mathbf{y}$ with dimensions $p$ and $q$ respectively. With $n$ independent observations of $\mathbf{z}$ at hand, we study the correlation between $\mathbf{x}$ and $\mathbf{y}$, from the perspective of the Canonical Correlation Analysis, under the high-dimensional setting: both $p$ and $q$ are proportional to the sample size $n$. In this paper, we focus on the case that...

Topics: Mathematics, Probability, Statistics Theory, Statistics

Source: http://arxiv.org/abs/1407.7194

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2.0

Jun 30, 2018
06/18

by
Aymeric Dieuleveut; Francis Bach

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We consider the random-design least-squares regression problem within the reproducing kernel Hilbert space (RKHS) framework. Given a stream of independent and identically distributed input/output data, we aim to learn a regression function within an RKHS $\mathcal{H}$, even if the optimal predictor (i.e., the conditional expectation) is not in $\mathcal{H}$. In a stochastic approximation framework where the estimator is updated after each observation, we show that the averaged unregularized...

Topics: Mathematics, Statistics Theory, Statistics

Source: http://arxiv.org/abs/1408.0361

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3.0

Jun 30, 2018
06/18

by
Ting Yan; Chenlei Leng; Ji Zhu

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Although asymptotic analyses of undirected network models based on degree sequences have started to appear in recent literature, it remains an open problem to study statistical properties of directed network models. In this paper, we provide for the first time a rigorous analysis of directed exponential random graph models using the in-degrees and out-degrees as sufficient statistics with binary as well as continuous weighted edges. We establish the uniform consistency and the asymptotic...

Topics: Mathematics, Statistics Theory, Statistics

Source: http://arxiv.org/abs/1408.1156

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3.0

Jun 30, 2018
06/18

by
Waheed U. Bajwa; Dustin G. Mixon

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Subspace-based signal processing traditionally focuses on problems involving a few subspaces. Recently, a number of problems in different application areas have emerged that involve a significantly larger number of subspaces relative to the ambient dimension. It becomes imperative in such settings to first identify a smaller set of active subspaces that contribute to the observation before further processing can be carried out. This problem of identification of a small set of active subspaces...

Topics: Mathematics, Computing Research Repository, Statistics Theory, Information Theory, Statistics

Source: http://arxiv.org/abs/1408.1469

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2.0

Jun 30, 2018
06/18

by
Torkel Erhardsson

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A $d$-dimensional RCA(1) process is a generalization of the $d$-dimensional AR(1) process, such that the coefficients $\{M_t;t=1,2,\ldots\}$ are i.i.d. random matrices. In the case $d=1$, under a nondegeneracy condition, Goldie and Maller gave necessary and sufficient conditions for the convergence in distribution of an RCA(1) process, and for the almost sure convergence of a closely related sum of random variables called a perpetuity. We here prove that under the condition $\Vert...

Topics: Mathematics, Statistics Theory, Statistics

Source: http://arxiv.org/abs/1403.3280

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3.0

Jun 30, 2018
06/18

by
Adityanand Guntuboyina

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We prove bounds for the covering numbers of classes of convex functions and convex sets in Euclidean space. Previous results require the underlying convex functions or sets to be uniformly bounded. We relax this assumption and replace it with weaker integral constraints. Existing results can be recovered as special cases of our results.

Topics: Statistics, Mathematics, Computing Research Repository, Information Theory, Statistics Theory,...

Source: http://arxiv.org/abs/1403.6922

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2.0

Jun 30, 2018
06/18

by
Olimjon Sharipov; Johannes Tewes; Martin Wendler

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A new test for structural changes in functional data is investigated. It is based on Hilbert space theory and critical values are deduced from bootstrap iterations. Thus a new functional central limit theorem for the block bootstrap in a Hilbert space is required. The test can also be used to detect changes in the marginal distribution of random vectors, which is supplemented by a simulation study. Our methods are applied to hydrological data from Germany.

Topics: Mathematics, Statistics Theory, Statistics

Source: http://arxiv.org/abs/1412.0446

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10.0

Jun 27, 2018
06/18

by
Thomas Mikosch; Yuwei Zhao

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We investigate the asymptotic properties of the integrated periodogram calculated from a sequence of indicator functions of dependent extremal events. An event in Euclidean space is extreme if it occurs far away from the origin. We use a regular variation condition on the underlying stationary sequence to make these notions precise. Our main result is a functional central limit theorem for the integrated periodogram of the indicator functions of dependent extremal events. The limiting process...

Topics: Statistics, Mathematics, Statistics Theory

Source: http://arxiv.org/abs/1503.04022

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7.0

Jun 28, 2018
06/18

by
Ilias Diakonikolas; Daniel M. Kane; Vladimir Nikishkin

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We give a general unified method that can be used for $L_1$ {\em closeness testing} of a wide range of univariate structured distribution families. More specifically, we design a sample optimal and computationally efficient algorithm for testing the equivalence of two unknown (potentially arbitrary) univariate distributions under the $\mathcal{A}_k$-distance metric: Given sample access to distributions with density functions $p, q: I \to \mathbb{R}$, we want to distinguish between the cases...

Topics: Statistics, Statistics Theory, Data Structures and Algorithms, Information Theory, Computing...

Source: http://arxiv.org/abs/1508.05538

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5.0

Jun 27, 2018
06/18

by
Agathe Guilloux; Sarah Lemler; Marie-Luce Taupin

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The purpose of this article is to provide an adaptive estimator of the baseline function in the Cox model with high-dimensional covariates. We consider a two-step procedure : first, we estimate the regression parameter of the Cox model via a Lasso procedure based on the partial log-likelihood, secondly, we plug this Lasso estimator into a least-squares type criterion and then perform a model selection procedure to obtain an adaptive penalized contrast estimator of the baseline function. Using...

Topics: Applications, Statistics, Mathematics, Statistics Theory

Source: http://arxiv.org/abs/1503.00226

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3.0

Jun 29, 2018
06/18

by
Pierre C. Bellec; Alexandre B. Tsybakov

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This paper considers the penalized least squares estimator with arbitrary convex penalty. When the observation noise is Gaussian, we show that the prediction error is a subgaussian random variable concentrated around its median. We apply this concentration property to derive sharp oracle inequalities for the prediction error of the LASSO, the group LASSO and the SLOPE estimators, both in probability and in expectation. In contrast to the previous work on the LASSO type methods, our oracle...

Topics: Statistics, Statistics Theory, Mathematics

Source: http://arxiv.org/abs/1609.06675