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.