Related papers: Robust high-dimensional Gaussian and bootstrap app…
We consider two problems of estimation in high-dimensional Gaussian models. The first problem is that of estimating a linear functional of the means of $n$ independent $p$-dimensional Gaussian vectors, under the assumption that most of…
This paper deals with Gibbs samplers that include high dimensional conditional Gaussian distributions. It proposes an efficient algorithm that avoids the high dimensional Gaussian sampling and relies on a random excursion along a small set…
Student's $t$ statistic is finding applications today that were never envisaged when it was introduced more than a century ago. Many of these applications rely on properties, for example robustness against heavy tailed sampling…
In high-dimensional time series analysis, Gaussian approximation (GA) schemes under various distance measures or on various collections of subsets of the Euclidean space play a fundamental role in a wide range of statistical inference…
This article reviews recent progress in high-dimensional bootstrap. We first review high-dimensional central limit theorems for distributions of sample mean vectors over the rectangles, bootstrap consistency results in high dimensions, and…
Data subject to heavy-tailed errors are commonly encountered in various scientific fields, especially in the modern era with explosion of massive data. To address this problem, procedures based on quantile regression and Least Absolute…
We present new estimators of the mean of a real valued random variable, based on PAC-Bayesian iterative truncation. We analyze the non-asymptotic minimax properties of the deviations of estimators for distributions having either a bounded…
The problem of constructing a simultaneous confidence surface for the 2-dimensional mean function of a non-stationary functional time series is challenging as these bands can not be built on classical limit theory for the maximum absolute…
Under certain conditions, the largest eigenvalue of a sample covariance matrix undergoes a well-known phase transition when the sample size $n$ and data dimension $p$ diverge proportionally. In the subcritical regime, this eigenvalue has…
We consider the problem of Gaussian multiplier bootstrap procedures for the $k$th largest statistics and functions of the top $k$ order statistics, which are commonly encountered in high-dimensional statistical inference. Such a problem has…
Big data can easily be contaminated by outliers or contain variables with heavy-tailed distributions, which makes many conventional methods inadequate. To address this challenge, we propose the adaptive Huber regression for robust…
Assume that $X_{1}, \ldots, X_{N}$ is an $\varepsilon$-contaminated sample of $N$ independent Gaussian vectors in $\mathbb{R}^d$ with mean $\mu$ and covariance $\Sigma$. In the strong $\varepsilon$-contamination model we assume that the…
This paper addresses the question of when projections of a high-dimensional random vector are approximately Gaussian. This problem has been studied previously in the context of high-dimensional data analysis, where the focus is on…
We study the problem of robustly estimating the mean of a $d$-dimensional distribution given $N$ examples, where most coordinates of every example may be missing and $\varepsilon N$ examples may be arbitrarily corrupted. Assuming each…
In this paper we consider the construction of simultaneous confidence bands for the spectral density of a stationary time series using a Gaussian approximation for classical lag-window spectral density estimators evaluated at the set of all…
Robust methods, though ubiquitous in practice, are yet to be fully understood in the context of regularized estimation and high dimensions. Even simple questions become challenging very quickly. For example, classical statistical theory…
We derive strong approximations to the supremum of the non-centered empirical process indexed by a possibly unbounded VC-type class of functions by the suprema of the Gaussian and bootstrap processes. The bounds of these approximations are…
In this paper, we propose self-tuned robust estimators for estimating the mean of heavy-tailed distributions, which refer to distributions with only finite variances. Our approach introduces a new loss function that considers both the mean…
This paper investigates theoretical properties of subsampling and hashing as tools for approximate Euclidean norm-preserving embeddings for vectors with (unknown) additive Gaussian noises. Such embeddings are sometimes called…
Several new methods have been proposed for performing valid inference after model selection. An older method is sampling splitting: use part of the data for model selection and part for inference. In this paper we revisit sample splitting…