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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

Statistical inference in high dimensional settings has recently attracted enormous attention within the literature. However, most published work focuses on the parametric linear regression problem. This paper considers an important…

Methodology · Statistics 2019-11-14 Qi Gao , Randy C. S. Lai , Thomas C. M. Lee , Yao Li

Motivated by statistical inference problems in high-dimensional time series data analysis, we first derive non-asymptotic error bounds for Gaussian approximations of sums of high-dimensional dependent random vectors on hyper-rectangles,…

Statistics Theory · Mathematics 2024-06-05 Jinyuan Chang , Xiaohui Chen , Mingcong Wu

This paper presents a selective survey of recent developments in statistical inference and multiple testing for high-dimensional regression models, including linear and logistic regression. We examine the construction of confidence…

Methodology · Statistics 2023-01-26 T. Tony Cai , Zijian Guo , Yin Xia

This paper proposes a decorrelation-based approach to test hypotheses and construct confidence intervals for the low dimensional component of high dimensional proportional hazards models. Motivated by the geometric projection principle, we…

Machine Learning · Statistics 2014-12-17 Ethan X. Fang , Yang Ning , Han Liu

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

We endeavour to estimate numerous multi-dimensional means of various probability distributions on a common space based on independent samples. Our approach involves forming estimators through convex combinations of empirical means derived…

Machine Learning · Statistics 2025-03-11 Gilles Blanchard , Jean-Baptiste Fermanian , Hannah Marienwald

The Support Vector Machine (SVM) is one of the most widely used classification methods. In this paper, we consider the soft-margin SVM used on data points with independent features, where the sample size $n$ and the feature dimension $p$…

Machine Learning · Statistics 2019-08-02 Haoyang Liu

We study time-uniform statistical inference for parameters in stochastic approximation (SA), which encompasses a bunch of applications in optimization and machine learning. To that end, we analyze the almost-sure convergence rates of the…

Machine Learning · Statistics 2024-10-22 Chuhan Xie , Kaicheng Jin , Jiadong Liang , Zhihua Zhang

We consider the problem of fitting the parameters of a high-dimensional linear regression model. In the regime where the number of parameters $p$ is comparable to or exceeds the sample size $n$, a successful approach uses an…

Statistics Theory · Mathematics 2013-11-04 Adel Javanmard , Andrea Montanari

This paper examines the construction of confidence sets for parameters defined as linear functionals of a function of W and X whose conditional mean given Z and X equals the conditional mean of another variable Y given Z and X. Many…

Statistics Theory · Mathematics 2025-08-08 Ezequiel Smucler , James M. Robins , Andrea Rotnitzky

Nonparametric two-stage procedures to construct fixed-width confidence intervals are studied to quantify uncertainty. It is shown that the validity of the random central limit theorem (RCLT) accompanied by a consistent and asymptotically…

Statistics Theory · Mathematics 2019-10-08 Yuan-Tsung Chang , Ansgar Steland

Inference on the parametric part of a semiparametric model is no trivial task. If one approximates the infinite dimensional part of the semiparametric model by a parametric function, one obtains a parametric model that is in some sense…

Statistics Theory · Mathematics 2025-09-23 Adam Lee , Emil A. Stoltenberg , Per A. Mykland

We develop a general assumption-lean framework for constructing uniformly valid confidence sets for functionals defined by moment equalities, referred to as $Z$-functionals. Our approach combines self-normalized statistics with a test…

Statistics Theory · Mathematics 2025-07-11 Woonyoung Chang , Arun Kumar Kuchibhotla

We study high-dimensional linear models with error-in-variables. Such models are motivated by various applications in econometrics, finance and genetics. These models are challenging because of the need to account for measurement errors to…

Statistics Theory · Mathematics 2017-03-03 Alexandre Belloni , Victor Chernozhukov , Abhishek Kaul

We suggest general methods to construct asymptotically uniformly valid confidence intervals post-model-selection. The constructions are based on principles recently proposed by Berk et al. (2013). In particular the candidate models used can…

Statistics Theory · Mathematics 2017-11-15 François Bachoc , David Preinerstorfer , Lukas Steinberger

High-dimensional linear models with endogenous variables play an increasingly important role in recent econometric literature. In this work we allow for models with many endogenous variables and many instrument variables to achieve…

Econometrics · Economics 2019-08-30 Alexandre Belloni , Christian Hansen , Whitney Newey

In this article, we investigate the asymptotic properties of Bayesian multiple testing procedures under general dependent setup, when the sample size and the number of hypotheses both tend to infinity. Specifically, we investigate strong…

Statistics Theory · Mathematics 2020-05-14 Noirrit Kiran Chandra , Sourabh Bhattacharya

In the context of linear regression, we construct a data-driven convex loss function with respect to which empirical risk minimisation yields optimal asymptotic variance in the downstream estimation of the regression coefficients. At the…

Statistics Theory · Mathematics 2025-05-29 Oliver Y. Feng , Yu-Chun Kao , Min Xu , Richard J. Samworth

In this paper, we introduce an innovative testing procedure for assessing individual hypotheses in high-dimensional linear regression models with measurement errors. This method remains robust even when either the X-model or Y-model is…

Methodology · Statistics 2025-01-14 Shijie Cui , Xu Guo , Songshan Yang , Zhe Zhang