Confidence Intervals for Maximin Effects in Inhomogeneous Large-Scale Data

TL;DR

This paper develops asymptotically valid confidence intervals for maximin effects in large-scale, inhomogeneous data, addressing the challenge of non-identical distributions across data groups.

Contribution

It introduces a method to construct confidence regions for maximin effects, extending previous point estimators to provide statistical inference.

Findings

Confidence regions are asymptotically valid.

Method effectively captures effects common across diverse data groups.

Addresses inhomogeneity in large-scale data analysis.

Abstract

One challenge of large-scale data analysis is that the assumption of an identical distribution for all samples is often not realistic. An optimal linear regression might, for example, be markedly different for distinct groups of the data. Maximin effects have been proposed as a computationally attractive way to estimate effects that are common across all data without fitting a mixture distribution explicitly. So far just point estimators of the common maximin effects have been proposed in Meinshausen and B\"uhlmann (2014). Here we propose asymptotically valid confidence regions for these effects.