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We consider linear regression in the high-dimensional regime where the number of observations $n$ is smaller than the number of parameters $p$. A very successful approach in this setting uses $\ell_1$-penalized least squares (a.k.a. the…

Methodology · Statistics 2014-02-05 Adel Javanmard , Andrea Montanari

This paper introduces a new framework to study the asymptotical behavior of the empirical distribution function (e.d.f.) of Gaussian vector components, whose correlation matrix $\Gamma^{(m)}$ is dimension-dependent. Hence, by contrast with…

Statistics Theory · Mathematics 2013-05-07 Sylvain Delattre , Etienne Roquain

In the inverse Gaussian sequence space model with additional noisy observations of the operator, we derive nonasymptotic minimax radii of testing for ellipsoid-type alternatives simultaneously for both the signal detection problem (testing…

Statistics Theory · Mathematics 2020-02-19 Sandra Schluttenhofer , Jan Johannes

We study the estimation of the covariance matrix $\Sigma$ of a $p$-dimensional normal random vector based on $n$ independent observations corrupted by additive noise. Only a general nonparametric assumption is imposed on the distribution of…

Statistics Theory · Mathematics 2018-03-28 Denis Belomestny , Mathias Trabs , Alexandre B. Tsybakov

We consider testing for presence of a signal in Gaussian white noise with intensity 1/sqrt(n), when the alternatives are given by smoothness ellipsoids with an L2-ball of (squared) radius rho removed. It is known that, for a fixed Sobolev…

Statistics Theory · Mathematics 2020-08-11 Pengsheng Ji , Michael Nussbaum

We investigate the asymptotics of eigenvalues of sample covariance matrices associated with a class of non-independent Gaussian processes (separable and temporally stationary) under the Kolmogorov asymptotic regime. The limiting spectral…

Probability · Mathematics 2019-10-11 Tiebin Mi , Robert Caiming Qiu

When inferring parameters from a Gaussian-distributed data set by computing a likelihood, a covariance matrix is needed that describes the data errors and their correlations. If the covariance matrix is not known a priori, it may be…

Cosmology and Nongalactic Astrophysics · Physics 2016-01-27 Elena Sellentin , Alan F. Heavens

Consider the Gaussian vector model with mean value {\theta}. We study the twin problems of estimating the number |{\theta}|_0 of non-zero components of {\theta} and testing whether |{\theta}|_0 is smaller than some value. For testing, we…

Statistics Theory · Mathematics 2017-03-02 Alexandra Carpentier , Nicolas Verzelen

In this paper, we consider the problem of determining the presence of a given signal in a high-dimensional observation with unknown covariance matrix by using an adaptive matched filter. Traditionally such filters are formed from the sample…

Statistics Theory · Mathematics 2021-12-06 Benjamin D. Robinson , Robert Malinas , Alfred O. Hero

Due to their parsimony, separable covariance models have been popular in modeling matrix-variate data. However, the inference from such a model may be misleading if the population covariance matrix $\Sigma$ is actually non-separable,…

Statistics Theory · Mathematics 2026-05-05 Bongjung Sung , Peter D. Hoff

In many statistical signal processing applications, the estimation of nuisance parameters and parameters of interest is strongly linked to the resulting performance. Generally, these applications deal with complex data. This paper focuses…

Applications · Statistics 2016-08-24 Melanie Mahot , Philippe Forster , Frederic Pascal , Jean-Philippe Ovarlez

Covariance matrix estimation concerns the problem of estimating the covariance matrix from a collection of samples, which is of extreme importance in many applications. Classical results have shown that $O(n)$ samples are sufficient to…

Information Theory · Computer Science 2019-03-19 Wei Cui , Xu Zhang , Yulong Liu

Minimax detection of Gaussian stochastic sequences (signals) with unknown covariance matrices is studied. For a fixed false alarm probability (1-st kind error probability), the performance of the minimax detection is being characterized by…

Information Theory · Computer Science 2021-04-14 M. V. Burnashev

We consider a general class of statistical experiments, in which an $n$-dimensional centered Gaussian random variable is observed and its covariance matrix is the parameter of interest. The covariance matrix is assumed to be…

Statistics Theory · Mathematics 2025-01-17 Cristina Butucea , Alexander Meister , Angelika Rohde

The problem of detecting changes in covariance for a single pair of features has been studied in some detail, but may be limited in importance or general applicability. In contrast, testing equality of covariance matrices of a {\it set} of…

Methodology · Statistics 2017-12-12 Yi-Hui Zhou

Motivated by applications in cybersecurity and epidemiology, we consider the problem of detecting an abrupt change in the intensity of a Poisson process, characterised by a jump (non transitory change) or a bump (transitory change) from…

Statistics Theory · Mathematics 2021-06-09 Magalie Fromont , Fabrice Grela , Ronan Le Guével

In this work we consider the problem of estimating a high-dimensional $p \times p$ covariance matrix $\Sigma$, given $n$ observations of confounded data with covariance $\Sigma + \Gamma \Gamma^T$, where $\Gamma$ is an unknown $p \times q$…

Methodology · Statistics 2019-12-03 Rajen D. Shah , Benjamin Frot , Gian-Andrea Thanei , Nicolai Meinshausen

We consider Gaussian measures $\mu, \tilde{\mu}$ on a separable Hilbert space, with fractional-order covariance operators $A^{-2\beta}$ resp. $\tilde{A}^{-2\tilde{\beta}}$, and derive necessary and sufficient conditions on $A, \tilde{A}$…

Probability · Mathematics 2023-07-19 David Bolin , Kristin Kirchner

Missing data occur frequently in a wide range of applications. In this paper, we consider estimation of high-dimensional covariance matrices in the presence of missing observations under a general missing completely at random model in the…

Methodology · Statistics 2016-05-17 T. Tony Cai , Anru Zhang

We consider a model where a signal (discrete or continuous) is observed with an additive Gaussian noise process. The signal is issued from a linear combination of a finite but increasing number of translated features. The features are…

Statistics Theory · Mathematics 2024-07-23 Cristina Butucea , Jean-François Delmas , Anne Dutfoy , Clément Hardy