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This paper develops asymptotic normality results for individual coordinates of robust M-estimators with convex penalty in high-dimensions, where the dimension $p$ is at most of the same order as the sample size $n$, i.e, $p/n\le\gamma$ for…

Statistics Theory · Mathematics 2021-07-09 Pierre C Bellec , Yiwei Shen , Cun-Hui Zhang

This paper addresses the asymptotic behavior of a particular type of information-plus-noise-type matrices, where the column and row number of the matrices are large and of the same order, while signals are diverged and time delays of the…

Information Theory · Computer Science 2019-03-11 Guanping Lu , Jinsong Wu , Robert C. Qiu

We consider the problem of robustly testing the norm of a high-dimensional sparse signal vector under two different observation models. In the first model, we are given $n$ i.i.d. samples from the distribution…

Information Theory · Computer Science 2022-11-08 Anand Jerry George , Clément L. Canonne

We provide finite-sample distribution approximations, that are uniform in the parameter, for inference in linear mixed models. Focus is on variances and covariances of random effects in cases where existing theory fails because their…

Statistics Theory · Mathematics 2025-07-29 Karl Oskar Ekvall , Matteo Bottai

For estimating the unknown parameters in an unstable autoregressive AR(p), the paper proposes sequential least squares estimates with a special stopping time defined by the trace of the observed Fisher information matrix. The limiting…

Statistics Theory · Mathematics 2008-10-07 Leonid Galtchouk , Victor Konev

This manuscript goes through the fundamental connections between statistical mechanics and estimation theory by focusing on the particular problem of compressive sensing. We first show that the asymptotic analysis of a sparse recovery…

Information Theory · Computer Science 2022-12-21 Ali Bereyhi , Ralf R. Müller , Hermann Schulz-Baldes

We consider the high-dimensional linear regression model $Y = X \beta^0 + \epsilon$ with Gaussian noise $\epsilon$ and Gaussian random design $X$. We assume that $\Sigma:= E X^T X / n$ is non-singular and write its inverse as $\Theta :=…

Statistics Theory · Mathematics 2018-08-22 Sara van de Geer

We consider the adaptive Lasso estimator with componentwise tuning in the framework of a low-dimensional linear regression model. In our setting, at least one of the components is penalized at the rate of consistent model selection and…

Statistics Theory · Mathematics 2025-11-11 Nicolai Amann , Ulrike Schneider

We consider the problem of sparsity testing in the high-dimensional linear regression model. The problem is to test whether the number of non-zero components (aka the sparsity) of the regression parameter $\theta^*$ is less than or equal to…

Statistics Theory · Mathematics 2020-04-24 Alexandra Carpentier , Nicolas Verzelen

We consider a sparse linear regression model with unknown symmetric error under the high-dimensional setting. The true error distribution is assumed to belong to the locally $\beta$-H\"{o}lder class with an exponentially decreasing tail,…

Statistics Theory · Mathematics 2020-09-01 Kyoungjae Lee , Minwoo Chae , Lizhen Lin

Multivariate elliptically-contoured distributions are widely used for modeling correlated and non-Gaussian data. In this work, we study the kurtosis of the elliptical model, which is an important parameter in many statistical analysis.…

Statistics Theory · Mathematics 2024-08-23 Bowen Zhou , Peirong Xu , Cheng Wang

We study semi-parametric estimation of the population mean when data is observed missing at random (MAR) in the $n < p$ "inconsistency regime", in which neither the outcome model nor the propensity/missingness model can be estimated…

Statistics Theory · Mathematics 2023-09-06 Michael Celentano , Martin J. Wainwright

Sparsity promoting norms are frequently used in high dimensional regression. A limitation of such Lasso-type estimators is that the optimal regularization parameter depends on the unknown noise level. Estimators such as the concomitant…

Machine Learning · Statistics 2020-09-04 Quentin Bertrand , Mathurin Massias , Alexandre Gramfort , Joseph Salmon

Asymptotic optimality is a key theoretical property in model averaging. Due to technical difficulties, existing studies rely on restricted weight sets or the assumption that there is no true model with fixed dimensions in the candidate set.…

Statistics Theory · Mathematics 2024-11-15 Wenchao Xu , Xinyu Zhang

We propose a principal components regression method based on maximizing a joint pseudo-likelihood for responses and predictors. Our method uses both responses and predictors to select linear combinations of the predictors relevant for the…

Methodology · Statistics 2021-08-10 Karl Oskar Ekvall

The asymptotic solution to the problem of comparing the means of two heteroscedastic populations, based on two random samples from the populations, hinges on the pivot underpinning the construction of the confidence interval and the test…

Statistics Theory · Mathematics 2017-10-30 Rajeshwari Majumdar , Suman Majumdar

Consider a bipartite network where $N$ consumers choose to buy or not to buy $M$ different products. This paper considers the properties of the logistic regression of the $N\times M$ array of i-buys-j purchase decisions,…

Econometrics · Economics 2020-10-12 Bryan S. Graham

This paper studies the properties of linear regression on centrality measures when network data is sparse and observed with error. We make three contributions in this setting. First, we show that OLS estimators can become inconsistent under…

Econometrics · Economics 2026-03-18 Yong Cai

Statistical models that possess symmetry arise in diverse settings such as random fields associated to geophysical phenomena, exchangeable processes in Bayesian statistics, and cyclostationary processes in engineering. We formalize the…

Statistics Theory · Mathematics 2011-12-01 Parikshit Shah , Venkat Chandrasekaran

Modern technologies are producing a wealth of data with complex structures. For instance, in two-dimensional digital imaging, flow cytometry, and electroencephalography, matrix type covariates frequently arise when measurements are obtained…

Methodology · Statistics 2013-10-22 Hua Zhou , Lexin Li