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In this paper, we introduce new parametric and semiparametric regression techniques for a recurrent event process subject to random right censoring. We develop models for the cumula- tive mean function and provide asymptotically normal…

Statistics Theory · Mathematics 2015-03-17 Olivier Bouaziz , Ségolen Geffray , Olivier Lopez

We study high-dimensional regression with missing entries in the covariates. A common strategy in practice is to \emph{impute} the missing entries with an appropriate substitute and then implement a standard statistical procedure acting as…

Statistics Theory · Mathematics 2020-01-28 Kabir Aladin Chandrasekher , Ahmed El Alaoui , Andrea Montanari

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

Inspired by the complexity of certain real-world datasets, this article introduces a novel flexible linear spline index regression model. The model posits piecewise linear effects of an index on the response, with continuous changes…

Methodology · Statistics 2024-09-04 Lianqiang Qu , Long Lv , Meiling Hao , Liuquan Sun

In the common partially linear single-index model we establish a Bahadur representation for a smoothing spline estimator of all model parameters and use this result to prove the joint weak convergence of the estimator of the index link…

Statistics Theory · Mathematics 2024-07-03 Jiajun Tang , Holger Dette

In functional linear regression, the parameters estimation involves solving a non necessarily well-posed problem and it has points of contact with a range of methodologies, including statistical smoothing, deconvolution and projection on…

Statistics Theory · Mathematics 2018-01-04 Andrea Ghiglietti , Francesca Ieva , Anna Maria Paganoni , Giacomo Aletti

This paper discusses a nonparametric regression model that naturally generalizes neural network models. The model is based on a finite number of one-dimensional transformations and can be estimated with a one-dimensional rate of…

Statistics Theory · Mathematics 2008-12-18 Joel L. Horowitz , Enno Mammen

Functional linear and single-index models are core regression methods in functional data analysis and are widely used for performing regression in a wide range of applications when the covariates are random functions coupled with scalar…

Statistics Theory · Mathematics 2024-03-28 Krishnakumar Balasubramanian , Hans-Georg Müller , Bharath K. Sriperumbudur

We investigate the problem of statistical inference for logistic regression with high-dimensional covariates in settings where dependence among individuals is induced by an underlying Markov random field. Going beyond the pairwise…

Statistics Theory · Mathematics 2026-03-23 Josh Miles , Sohom Bhattacharya

Single-Index Models are high-dimensional regression problems with planted structure, whereby labels depend on an unknown one-dimensional projection of the input via a generic, non-linear, and potentially non-deterministic transformation. As…

Machine Learning · Computer Science 2024-03-14 Alex Damian , Loucas Pillaud-Vivien , Jason D. Lee , Joan Bruna

Generalized Linear Models (GLMs) and Single Index Models (SIMs) provide powerful generalizations of linear regression, where the target variable is assumed to be a (possibly unknown) 1-dimensional function of a linear predictor. In general,…

Artificial Intelligence · Computer Science 2011-04-14 Sham Kakade , Adam Tauman Kalai , Varun Kanade , Ohad Shamir

We consider linear regression in the high-dimensional regime where the number of observations $n$ is smaller than the number of parameters $p$. A very successful approach in this setting uses $\ell_1$-penalized least squares (a.k.a. the…

Methodology · Statistics 2014-02-05 Adel Javanmard , Andrea Montanari

This paper studies inference in the high-dimensional linear regression model with outliers. Sparsity constraints are imposed on the vector of coefficients of the covariates. The number of outliers can grow with the sample size while their…

Statistics Theory · Mathematics 2021-02-08 Jad Beyhum

We consider estimation and inference in a single index regression model with an unknown convex link function. We introduce a convex and Lipschitz constrained least squares estimator (CLSE) for both the parametric and the nonparametric…

Statistics Theory · Mathematics 2021-01-15 Arun K. Kuchibhotla , Rohit K. Patra , Bodhisattva Sen

For statistical inference on regression models with a diverging number of covariates, the existing literature typically makes sparsity assumptions on the inverse of the Fisher information matrix. Such assumptions, however, are often…

Methodology · Statistics 2021-06-08 Lu Xia , Bin Nan , Yi Li

We study convex empirical risk minimization for high-dimensional inference in binary models. Our first result sharply predicts the statistical performance of such estimators in the linear asymptotic regime under isotropic Gaussian features.…

Statistics Theory · Mathematics 2020-02-27 Hossein Taheri , Ramtin Pedarsani , Christos Thrampoulidis

We study a linear observation model with an unknown permutation called \textit{permuted/shuffled linear regression}, where responses and covariates are mismatched and the permutation forms a discrete, factorial-size parameter. The…

Statistics Theory · Mathematics 2026-01-23 Hirofumi Ota , Masaaki Imaizumi

This paper presents a unified geometric framework for the statistical analysis of a general ill-posed linear inverse model which includes as special cases noisy compressed sensing, sign vector recovery, trace regression, orthogonal matrix…

Statistics Theory · Mathematics 2020-07-27 T. Tony Cai , Tengyuan Liang , Alexander Rakhlin

We developed a statistical inference method applicable to a broad range of generalized linear models (GLMs) in high-dimensional settings, where the number of unknown coefficients scales proportionally with the sample size. Although a…

Statistics Theory · Mathematics 2024-05-24 Kazuma Sawaya , Yoshimasa Uematsu , Masaaki Imaizumi

We consider the complex data modeling problem motivated by the zero-inflated and overdispersed data from microbiome studies. Analyzing how microbiome abundance is associated with human biological features, such as BMI, is of great…

Methodology · Statistics 2025-03-31 Zirui Wang , Tianying Wang