Inference on the change point estimator of variance in measurement error models*

Abstract

In this paper, we present a new estimator of the change point in variance of measurement errors in terms of U-statistics based on characteristic functions. We also investigate the strong consistency and convergence rates of the estimator. In addition, we develop the asymptotic distribution of the change point estimator under local alternative hypothesis, which is a two-side Brownian motion with a drift. Simulation results show that our estimator is significantly better than the estimator posed in [C.L. Dong et al., An estimate of a change point in variance of measurement errors and its convergence rate, Commun. Stat., Theory Methods, 44(4):790–797, 2015].