Change point detection for nonparametric regression under strongly mixing process

Hajek–Renyi-type inequality for $(\alpha , \beta )$-mixing sequences and its application to change-point model

“…For example, Horváth and Kokoszka [9] studied the asymptotic distribution of the CUSUM estimator of the change point for a stationary Gaussian random variable with long-range dependencies; Lavielle [14] presented some convergence results for the minimum contrast estimator in a problem of the change-point estimation in the case of strongly mixing and strongly dependent processes; Hariz and Wylie [8] established a unified framework for estimating the change point in the mean of stationary sequences and gave the rate of convergence for the CUSUM estimator; Shi et al [22] investigated the strong convergence and the corresponding rate for the CUSUM estimator of the change point under NA sequences and proposed an iterative algorithm for searching the location of a change point. More recent studies on the change-point analysis can be referred to Horváth and Rice [10], Jin et al [12], Messer et al [17], Xu et al [25], Yang et al [26], Ding et al [5], and the references therein. In this section, we investigate the CUSUMtype estimator of mean change-point models based on (α, β)-mixing sequences by using the Hajek-Renyi-type inequality we established previously.…”