Data‐driven estimation for multithreshold accelerated failure time model

This article develops a novel estimation framework for the multithreshold accelerated failure time model, which has distinct linear forms within different subdomains. One major challenge is to determine the number of threshold effects. We first show the selection consistency of a modified Bayesian information criterion under mild conditions. It is useful sometimes but heavily depends on the penalization magnitude, which usually varies from the model configuration and data distribution. To address this issue, we leverage a cross‐validation criterion alongside an order‐preserved sample‐splitting scheme to yield a consistent estimation. The new criterion is completely data driven without additional parameters and thus robust to model setting and data distributions. The asymptotic properties for the parameter estimates are also carefully established. Additionally, we propose an efficient score‐type test to examine the existence of threshold effects. The new statistic is free of estimating any potential threshold effects and is thus suitable for multithreshold scenarios. Numerical experiments validate the reliable finite‐sample performance of our methodologies, which corroborates the theoretical results.