相关论文: Optimal Shrinkage Estimator for High-Dimensional M…

This work is concerned with the estimation of multidimensional regression and the asymptotic behaviour of the test involved in selecting models. The main problem with such models is that we need to know the covariance matrix of the noise to…

We consider shrinkage estimation of higher order Hilbert space valued Bochner integrals in a non-parametric setting. We propose estimators that shrink the $U$-statistic estimator of the Bochner integral towards a pre-specified target…

Let $X_1, \ldots, X_n\in\mathbb{R}^p$ be i.i.d. random vectors. We aim to perform simultaneous inference for the mean vector $\mathbb{E} (X_i)$ with finite polynomial moments and an ultra high dimension. Our approach is based on the…

We study the optimal linear prediction of a random function that takes values in an infinite dimensional Hilbert space. We begin by characterizing the mean square prediction error (MSPE) associated with a linear predictor and discussing the…

In this paper, we develop new statistical theory for probabilistic principal component analysis models in high dimensions. The focus is the estimation of the noise variance, which is an important and unresolved issue when the number of…

We study the fundamental problem of high-dimensional mean estimation in a robust model where a constant fraction of the samples are adversarially corrupted. Recent work gave the first polynomial time algorithms for this problem with…

This work develops non-asymptotic theory for estimation of the long-run variance matrix and its inverse, the so-called precision matrix, for high-dimensional time series under general assumptions on the dependence structure including…

In recent years, shrinkage priors have received much attention in high-dimensional data analysis from a Bayesian perspective. Compared with widely used spike-and-slab priors, shrinkage priors have better computational efficiency. But the…

We study the problem of high-dimensional robust mean estimation in the presence of a constant fraction of adversarial outliers. A recent line of work has provided sophisticated polynomial-time algorithms for this problem with…

We establish large sample approximations for an arbitray number of bilinear forms of the sample variance-covariance matrix of a high-dimensional vector time series using $ \ell_1$-bounded and small $\ell_2$-bounded weighting vectors.…

In this paper, we consider directly estimating the eigenvalues of precision matrix, without inverting the corresponding estimator for the eigenvalues of covariance matrix. We focus on a general asymptotic regime, i.e., the large dimensional…

This article studies two regularized robust estimators of scatter matrices proposed (and proved to be well defined) in parallel in (Chen et al., 2011) and (Pascal et al., 2013), based on Tyler's robust M-estimator (Tyler, 1987) and on…

Differential entropy and log determinant of the covariance matrix of a multivariate Gaussian distribution have many applications in coding, communications, signal processing and statistical inference. In this paper we consider in the high…

A precision matrix is the inverse of a covariance matrix. In this paper, we study the problem of estimating the precision matrix with a known graphical structure under high-dimensional settings. We propose a simple estimator of the…

The determination of the covariance matrix and its inverse, the precision matrix, is critical in the statistical analysis of cosmological measurements. The covariance matrix is typically estimated with a limited number of simulations at…

We propose a general method for constructing confidence intervals and statistical tests for single or low-dimensional components of a large parameter vector in a high-dimensional model. It can be easily adjusted for multiplicity taking…

High-dimensional classification is a fundamentally important research problem in high-dimensional data analysis. In this paper, we derive a nonasymptotic rate for the minimax excess misclassification risk when feature dimension…

When shrinking a covariance matrix towards (a multiple) of the identity matrix, the trace of the covariance matrix arises naturally as the optimal scaling factor for the identity target. The trace also appears in other context, for example…

Analyzing large samples of high-dimensional data under dependence is a challenging statistical problem as long time series may have change points, most importantly in the mean and the marginal covariances, for which one needs valid tests.…

The covariance matrix plays a fundamental role in many modern exploratory and inferential statistical procedures, including dimensionality reduction, hypothesis testing, and regression. In low-dimensional regimes, where the number of…