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.

翻译：变平面估计量行为分析的一个关键挑战在于目标函数存在多个最小值点。针对这一非唯一性问题，本文提出了两种估计量。对每种估计量，我们建立了n阶收敛速率并推导了其极限分布。基于这些结果，我们提出了参数自助法推断流程。通过模拟实验验证了理论结果的有效性及自助法的有限样本表现。我们利用ACTG175艾滋病研究数据，将所提方法应用于精准医学中的潜在亚组识别实例。