Asymptotic distribution of the jump change-point estimator

The asymptotic distribution of the change-point estimator in a jump changepoint model is considered. For the jump change-point model Xi = a + θI{[nτ0] < i ≤ n} + ɛi, where ɛi (i = 1, ..., n) are independent identically distributed random variables with Eɛi = 0 and Var(ɛi) < ∞, with the help of the slip window method, the asymptotic distribution of the jump change-point estimator \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hat \tau$$\end{document} is studied under the condition of the local alternative hypothesis.