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Effect modification occurs when the effect of the treatment on an outcome varies according to the level of other covariates and often has important implications in decision making. When there are tens or hundreds of covariates, it becomes…

Methodology · Statistics 2021-11-23 Qingyuan Zhao , Dylan S. Small , Ashkan Ertefaie

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

We consider the least-square linear regression problem with regularization by the $\ell^1$-norm, a problem usually referred to as the Lasso. In this paper, we first present a detailed asymptotic analysis of model consistency of the Lasso in…

Machine Learning · Computer Science 2009-01-22 Francis Bach

We propose a novel approach to elicit the weight of a potentially non-stationary regressor in the consistent and oracle-efficient estimation of autoregressive models using the adaptive Lasso. The enhanced weight builds on a statistic that…

Methodology · Statistics 2024-07-23 Thilo Reinschlüssel , Martin C. Arnold

In this paper, we propose an adaptive group lasso procedure to efficiently estimate structural breaks in cointegrating regressions. It is well-known that the group lasso estimator is not simultaneously estimation consistent and model…

Econometrics · Economics 2021-04-21 Karsten Schweikert

Variable selection is one of the most important tasks in statistics and machine learning. To incorporate more prior information about the regression coefficients, the constrained Lasso model has been proposed in the literature. In this…

Optimization and Control · Mathematics 2019-03-13 Zengde Deng , Anthony Man-Cho So

In this paper, we derive non-asymptotic error bounds for the Lasso estimator when the penalty parameter for the estimator is chosen using $K$-fold cross-validation. Our bounds imply that the cross-validated Lasso estimator has nearly…

Statistics Theory · Mathematics 2020-02-07 Denis Chetverikov , Zhipeng Liao , Victor Chernozhukov

This paper contributes to the literature on treatment effects estimation with machine learning inspired methods by studying the performance of different estimators based on the Lasso. Building on recent work in the field of high-dimensional…

Econometrics · Economics 2018-05-15 Michael Zimmert

Many problems in signal processing require finding sparse solutions to under-determined, or ill-conditioned, linear systems of equations. When dealing with real-world data, the presence of outliers and impulsive noise must also be accounted…

Statistics Theory · Mathematics 2017-05-08 Jasin Machkour , Michael Muma , Bastian Alt , Abdelhak M. Zoubir

This article investigates a new parameter for the high-dimensional regression with noise: the distortion. This latter has attracted a lot of attention recently with the appearance of new deterministic constructions of 'almost'-Euclidean…

Statistics Theory · Mathematics 2012-10-01 Yohann de Castro

Expected shortfall is defined as the average over the tail below (or above) a certain quantile of a probability distribution. Expected shortfall regression provides powerful tools for learning the relationship between a response variable…

Methodology · Statistics 2025-01-03 Shushu Zhang , Xuming He , Kean Ming Tan , Wen-Xin Zhou

When a series of (related) linear models has to be estimated it is often appropriate to combine the different data-sets to construct more efficient estimators. We use $\ell_1$-penalized estimators like the Lasso or the Adaptive Lasso which…

Statistics Theory · Mathematics 2007-12-18 Lukas Meier , Peter Bühlmann

Sparse linear models are one of several core tools for interpretable machine learning, a field of emerging importance as predictive models permeate decision-making in many domains. Unfortunately, sparse linear models are far less flexible…

Machine Learning · Statistics 2024-01-03 Ryan Thompson , Amir Dezfouli , Robert Kohn

In this paper, we develop a novel high-dimensional coefficient estimation procedure based on high-frequency data. Unlike usual high-dimensional regression procedures such as LASSO, we additionally handle the heavy-tailedness of…

Methodology · Statistics 2025-10-22 Minseok Shin , Donggyu Kim

We consider a high-dimensional multi-outcome regression in which $q,$ possibly dependent, binary and continuous outcomes are regressed onto $p$ covariates. We model the observed outcome vector as a partially observed latent realization from…

Methodology · Statistics 2025-11-05 Soham Ghosh , Sameer K. Deshpande

In Ciuperca (2012) (Ciuperca. Model selection by LASSO methods in a change-point model, Stat. Papers, 2012; (in press)), the author considered a linear regression model with multiple change-points occurring at unknown times. In particular,…

Methodology · Statistics 2014-03-10 Fuqi Chen , Sévérien Nkurunziza

We propose a two step algorithm based on $\ell_1/\ell_0$ regularization for the detection and estimation of parameters of a high dimensional change point regression model and provide the corresponding rates of convergence for the change…

Methodology · Statistics 2019-01-18 Abhishek Kaul , Venkata K. Jandhyala , Stergios B. Fotopoulos

Selective inference methods are developed for group lasso estimators for use with a wide class of distributions and loss functions. The method includes the use of exponential family distributions, as well as quasi-likelihood modeling for…

Methodology · Statistics 2024-03-28 Yiling Huang , Sarah Pirenne , Snigdha Panigrahi , Gerda Claeskens

We study the estimation capacity of the generalized Lasso, i.e., least squares minimization combined with a (convex) structural constraint. While Lasso-type estimators were originally designed for noisy linear regression problems, it has…

Statistics Theory · Mathematics 2019-09-12 Martin Genzel , Gitta Kutyniok

We consider the linear regression problem, where the number $p$ of covariates is possibly larger than the number $n$ of observations $(x_{i},y_{i})_{i\leq i \leq n}$, under sparsity assumptions. On the one hand, several methods have been…

Statistics Theory · Mathematics 2009-06-08 Pierre Alquier , Mohamed Hebiri