English
Related papers

Related papers: Universality of estimators for high-dimensional li…

200 papers

New local linear estimators are proposed for a wide class of nonparametric regression models. The estimators are uniformly consistent regardless of satisfying traditional conditions of depen\-dence of design elements. The estimators are the…

Statistics Theory · Mathematics 2022-07-05 Yuliana Linke , Igor Borisov , Pavel Ruzankin , Vladimir Kutsenko , Elena Yarovaya , Svetlana Shalnova

In this paper, we derive the joint asymptotic distributions of functions of quantile estimators (the non-parametric sample quantile and the parametric location-scale quantile estimator) with functions of measure of dispersion estimators…

Statistics Theory · Mathematics 2019-04-29 Marcel Bräutigam , Marie Kratz

The recent thought-provoking paper by Hansen [2022, Econometrica] proved that the Gauss-Markov theorem continues to hold without the requirement that competing estimators are linear in the vector of outcomes. Despite the elegant proof, it…

Econometrics · Economics 2023-01-02 Lihua Lei , Jeffrey Wooldridge

Multivariate processes with long-range dependence properties can be encountered in many fields of application. Two fundamental characteristics in such frameworks are long-range dependence parameters and correlations between component time…

Statistics Theory · Mathematics 2022-04-07 Irène Gannaz

We consider component-wise equivariant estimation of order restricted location/scale parameters of a general bivariate distribution under quite general conditions on underlying distributions and the loss function. This paper unifies various…

Statistics Theory · Mathematics 2022-07-05 Naresh Garg , Neeraj Misra

It has been observed that the performances of many high-dimensional estimation problems are universal with respect to underlying sensing (or design) matrices. Specifically, matrices with markedly different constructions seem to achieve…

Information Theory · Computer Science 2023-07-24 Rishabh Dudeja , Subhabrata Sen , Yue M. Lu

This paper introduces a general framework for estimating variance components in the linear mixed models via general unbiased estimating equations, which include some well-used estimators such as the restricted maximum likelihood estimator.…

Methodology · Statistics 2021-05-18 Tatsuya Kubokawa , Shonosuke Sugasawa , Hiromasa Tamae , Sanjay Chaudhuri

Suppose X is a random vector, that is distributed uniformly in some n-dimensional convex set. It was conjectured that when the dimension n is very large, there exists a non-zero vector u, such that the distribution of the real random…

Metric Geometry · Mathematics 2009-11-11 B. Klartag

Riemannian Gaussian distributions were initially introduced as basic building blocks for learning models which aim to capture the intrinsic structure of statistical populations of positive-definite matrices (here called covariance…

Statistics Theory · Mathematics 2023-02-16 Salem Said , Simon Heuveline , Cyrus Mostajeran

An important challenge in statistical analysis concerns the control of the finite sample bias of estimators. For example, the maximum likelihood estimator has a bias that can result in a significant inferential loss. This problem is…

Statistics Theory · Mathematics 2019-11-04 Stéphane Guerrier , Mucyo Karemera , Samuel Orso , Maria-Pia Victoria-Feser

This paper proposes a desparsified GMM estimator for estimating high-dimensional regression models allowing for, but not requiring, many more endogenous regressors than observations. We provide finite sample upper bounds on the estimation…

Statistics Theory · Mathematics 2019-09-11 Mehmet Caner , Anders Bredahl Kock

We prove a general multidimensional invariance principle for a family of U-statistics based on freely independent non-commutative random variables of the type $U_n(S)$, where $U_n(x)$ is the $n$-th Chebyshev polynomial and $S$ is a standard…

Probability · Mathematics 2016-11-23 R. Simone

Instrumental variable models allow us to identify a causal function between covariates $X$ and a response $Y$, even in the presence of unobserved confounding. Most of the existing estimators assume that the error term in the response $Y$…

Machine Learning · Statistics 2022-09-23 Sorawit Saengkyongam , Leonard Henckel , Niklas Pfister , Jonas Peters

For random matrices with block correlation structure we show that the fluctuations of linear eigenvalue statistics are Gaussian on all mesoscopic scales with universal variance which coincides with that of the Gaussian unitary or Gaussian…

Probability · Mathematics 2023-06-30 Torben Krüger , Yuriy Nemish

In many applications of network analysis, it is important to distinguish between observed and unobserved factors affecting network structure. To this end, we develop spectral estimators for both unobserved blocks and the effect of…

Methodology · Statistics 2021-03-15 Angelo Mele , Lingxin Hao , Joshua Cape , Carey E. Priebe

General ridge estimators are widely used in the general linear model because they possess desirable properties such as linear sufficiency and linear admissibility. However, when the covariance matrix of the error term is partially unknown,…

Statistics Theory · Mathematics 2026-01-27 Hirai Mukasa

We derive a scale-free bound on the density of the maximum of a centered Gaussian vector. The basic bound is non-uniform, depends logarithmically on the dimension, and allows any covariance matrix. When the largest marginal variance is…

Statistics Theory · Mathematics 2026-05-29 Suhas Vijaykumar

We study high-dimensional distribution learning in an agnostic setting where an adversary is allowed to arbitrarily corrupt an $\varepsilon$-fraction of the samples. Such questions have a rich history spanning statistics, machine learning…

Data Structures and Algorithms · Computer Science 2019-03-18 Ilias Diakonikolas , Gautam Kamath , Daniel Kane , Jerry Li , Ankur Moitra , Alistair Stewart

Distributional approximations of (bi--) linear functions of sample variance-covariance matrices play a critical role to analyze vector time series, as they are needed for various purposes, especially to draw inference on the dependence…

Probability · Mathematics 2018-03-20 Ansgar Steland , Rainer von Sachs

We consider the problem of estimating the error variance in a general linear model when the error distribution is assumed to be spherically symmetric, but not necessary Gaussian. In particular we study the case of a scale mixture of…

Statistics Theory · Mathematics 2013-03-18 Yuzo Maruyama , William E. Strawderman