Inference for change-plane regression

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 demonstrate the proposed methods by applying them to latent subgroup identification in precision medicine using the ACTG175 AIDS study data.