Inference for change-plane regression

TL;DR

This paper addresses the challenge of non-uniqueness in change-plane regression estimators by proposing two new estimators, establishing their convergence rates, deriving their distributions, and validating their performance through simulations and real data application.

Contribution

It introduces two novel estimators for change-plane regression with multiple minimizers, providing their theoretical properties and a bootstrap inference method.

Findings

Both estimators achieve n-rate convergence.

The bootstrap procedure is validated through simulations.

Application to AIDS data demonstrates practical utility.

Abstract

A key challenge in analyzing the behavior of change-plane estimators is that the objective function has multiple minimizers. Two estimators are proposed to deal with this non-uniqueness. For each estimator, an n-rate of convergence is established, and the limiting distribution is derived. Based on these results, we provide a parametric bootstrap procedure for inference. The validity of our theoretical results and the finite sample performance of the bootstrap are demonstrated through simulation experiments. We illustrate the proposed methods to latent subgroup identification in precision medicine using the ACTG175 AIDS study data.