Related papers: A shrinkage estimation for large dimensional preci…
The main theme of this paper is a modification of the likelihood ratio test (LRT) for testing high dimensional covariance matrix. Recently, the correct asymptotic distribution of the LRT for a large-dimensional case (the case $p/n$…
Low-rank tensor models are widely used in statistics. However, most existing methods rely heavily on the assumption that data follows a sub-Gaussian distribution. To address the challenges associated with heavy-tailed distributions…
This paper introduces a neural network-based nonlinear shrinkage estimator of covariance matrices for the purpose of minimum variance portfolio optimization. It is a hybrid approach that integrates statistical estimation with machine…
Meta-learning involves training models on a variety of training tasks in a way that enables them to generalize well on new, unseen test tasks. In this work, we consider meta-learning within the framework of high-dimensional multivariate…
In this paper, we propose a random projection approach to estimate variance in kernel ridge regression. Our approach leads to a consistent estimator of the true variance, while being computationally more efficient. Our variance estimator is…
We address the problem of robust sparse estimation of the precision matrix for heavy-tailed distributions in high-dimensional settings. In such high-dimensional contexts, we observe that the covariance matrix can be approximated by a…
We propose a flexible class of models based on scale mixture of uniform distributions to construct shrinkage priors for covariance matrix estimation. This new class of priors enjoys a number of advantages over the traditional scale mixture…
We consider $L^2$-regularized linear (ridge) regression over a finite data sample $X$ with bounded covariance and linear prediction targets $y$ with additive isotropic noise of finite variance. We present an iterative procedure to compute…
In this paper we propose new approaches to estimating large dimensional monotone index models. This class of models has been popular in the applied and theoretical econometrics literatures as it includes discrete choice, nonparametric…
We propose a framework to shrink a user-specified characteristic of a precision matrix estimator that is needed to fit a predictive model. Estimators in our framework minimize the Gaussian negative loglikelihood plus an $L_1$ penalty on a…
We revisit the classical problem of estimating an unknown distribution from its samples by fitting a mixture model that minimizes cross-entropy loss. Framing the task as a stochastic convex optimization problem over the space of $ M…
Covariance matrices play a major role in statistics, signal processing and machine learning applications. This paper focuses on the \textit{semiparametric} covariance/scatter matrix estimation problem in elliptical distributions. The class…
This paper presents a simple shrinkage estimator of rates based on Bayesian methods. Our focus is on crime rates as a motivating example. The estimator shrinks each town's observed crime rate toward the country-wide average crime rate…
Low-rank matrix estimation under heavy-tailed noise is challenging, both computationally and statistically. Convex approaches have been proven statistically optimal but suffer from high computational costs, especially since robust loss…
Estimation of a high dimensional precision matrix is a critical problem to many areas of statistics including Gaussian graphical models and inference on high dimensional data. Working under the structural assumption of sparsity, we propose…
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.…
Shrinkage can effectively improve the condition number and accuracy of covariance matrix estimation, especially for low-sample-support applications with the number of training samples smaller than the dimensionality. This paper investigates…
A large empirical literature regresses outcomes on empirical Bayes shrinkage estimates of value-added, yet little is known about whether this approach leads to unbiased estimates and valid inference for the downstream regression…
There has been a surge of interest in developing robust estimators for models with heavy-tailed and bounded variance data in statistics and machine learning, while few works impose unbounded variance. This paper proposes two type of robust…
Low-rank matrix approximations are often used to help scale standard machine learning algorithms to large-scale problems. Recently, matrix coherence has been used to characterize the ability to extract global information from a subset of…