Inference without compatibility: using exponential weighting for inference on a parameter of a linear model
type: Item
instance of: scholarly article
title: Inference without compatibility: using exponential weighting for inference on a parameter of a linear model
zbMATH Open document ID: 1473.62251
DOI: 10.3150/20-BEJ1280
author: Michael Law
author: Yaacov Ritov
published in: Bernoulli
publication date: 2021-07-09T00:00:00Z
review text: The authors consider a partially linear model \(Y = X\beta + \mu + \epsilon\) with \(n\)-dimensional \(Y\) and \(q\)-dimensional \(\beta\). The parameter \(\beta\) is assumed to be low-dimensional, \(q<n\), but the random nuisance \(\mu\) is modeled by \(\mu = Z\gamma\) with a \(p\)-dimensional sparse vector \(\gamma\), where \(p\) is high-dimensional, \(p>n\). The aim of the authors is inference on \(\beta\), on the signal strength \(\sigma^2_\mu\) and on the noise variance \(\sigma^2_\epsilon\). Since the Lasso (least absolute shrinkage and selection operator) forms the basis for the procedure, certain assumptions must be made to ensure nice properties. Especially the so-called compatibility condition seems to be indispensible. The main contribution of this paper is proving that the compatibility condition is not necessary for the statistical problem. The authors are able to construct \(\sqrt n\)-consistent estimators for \(\beta\), \(\sigma^2_\mu\) and \(\sigma^2_\epsilon\). Their approach involves using exponential weighing to aggregate over all models of particular size. This is a computationally hard problem, but can be well approximated. To this end, the authors present an algorithm and simulation results which allow comparison with other estimators.
reviewed by: Wolfgang Näther
Mathematics Subject Classification ID: 62J07
Mathematics Subject Classification ID: 62G05
Mathematics Subject Classification ID: 62-08
zbMATH DE Number: 7370717
zbMATH Keywords: Lasso
zbMATH Keywords: compatibility condition
zbMATH Keywords: exponential weighting
zbMATH Keywords: inference
describes a project that uses: selectiveInference
describes a project that uses: EigenPrism
MaRDI profile type: Publication
Wikidata QID: Q115488543
cites work: Q4277836
cites work: Fixed Effects Testing in High-Dimensional Linear Mixed Models
cites work: Statistics for high-dimensional data. Methods, theory and applications.
cites work: Semisupervised Inference for Explained Variance in High Dimensional Linear Regression and its Applications
cites work: Double/debiased machine learning for treatment and structural parameters
cites work: High-dimensional inference: confidence intervals, \(p\)-values and R-software \texttt{hdi}
cites work: Variance estimation in high-dimensional linear models
cites work: Variance Estimation Using Refitted Cross-Validation in Ultrahigh Dimensional Regression
cites work: Sure Independence Screening for Ultrahigh Dimensional Feature Space
cites work: Q2716030
cites work: Inconsistency of Bayesian inference for misspecified linear models, and a proposal for repairing it
cites work: A tail inequality for quadratic forms of subgaussian random vectors
cites work: EigenPrism: Inference for High Dimensional Signal-to-Noise Ratios
cites work: Confidence Intervals and Hypothesis Testing for High-Dimensional Regression
cites work: Debiasing the Lasso: optimal sample size for Gaussian designs
cites work: Exact post-selection inference, with application to the Lasso
cites work: Information Theory and Mixing Least-Squares Regressions
cites work: Restricted eigenvalue properties for correlated Gaussian designs
cites work: A study of error variance estimation in Lasso regression
cites work: Exponential screening and optimal rates of sparse estimation
cites work: Scaled sparse linear regression
cites work: Q4864293
cites work: On the conditions used to prove oracle results for the Lasso
cites work: On asymptotically optimal confidence regions and tests for high-dimensional models
cites work: Confidence Intervals for Low Dimensional Parameters in High Dimensional Linear Models
full work available at URL: 20-bej1280
OpenAlex ID: W3160524352
description: scientific article; zbMATH DE number 7370717