Asymptotic Properties of the Maximum Smoothed Partial Likelihood Estimator in the Change-Plane Cox Model

TL;DR

This paper investigates the asymptotic properties of a new estimator in the change-plane Cox model, revealing near-parametric convergence rates and asymptotic normality for the regression parameter.

Contribution

It introduces a maximum smoothed partial likelihood estimator and characterizes its convergence rate and asymptotic distribution in the change-plane Cox model.

Findings

Convergence rate for classification parameter can approach 1/n.

Establishes asymptotic normality for the regression parameter.

Provides theoretical foundation for estimator's asymptotic behavior.

Abstract

The change-plane Cox model is a popular tool for the subgroup analysis of survival data. Despite the rich literature on this model, there has been limited investigation into the asymptotic properties of the estimators of the finite-dimensional parameter. Particularly, the convergence rate, not to mention the asymptotic distribution, has not been fully characterized for the general model where classification is based on multiple covariates. To bridge this theoretical gap, this study proposes a maximum smoothed partial likelihood estimator and establishes the following asymptotic properties. First, it shows that the convergence rate for the classification parameter can be arbitrarily close to 1/n up to a logarithmic factor under a certain condition on covariates and the choice of tuning parameter. Given this convergence rate result, it also establishes the asymptotic normality for the regression parameter.