Change point estimation in regression model with response missing at random

Abstract

Based on the approach of left and right kernel smoothing with unilateral kernel function, we, in this paper, define estimators of change point and jump size in nonparametric regression model with response missing at random. It is shown that the change point estimator is n-consistent and converges to the smallest maximizer of one-dimensional bilateral compound Poisson process, the jump size estimator is asymptotically normal. A simulation study is conducted to investigate the finite sample behavior for the proposed methods.

Keywords:

• Asymptotic normality
• change point
• compound Poisson process
• missing at random
• nonparametric regression model

AMS 2000 subject classifications:

• 62G08
• 62N02

Additional information

Funding

This research was supported by the National Social Science Foundation of China (17BTJ032).