Wavelet estimation of a regression function with a sharp change-point in heavy-tailed noise

This paper considers the problem of a wavelet method to estimate a sharp change point and a nonparametric regression function under random design, whose noise is heavy tailed infinite-varianced process. By using two-step method, we propose a truncation estimator of the change point, which can weaken the influence of outliers. Moreover, the convergence rate is established. Finally we obtain a wavelet estimator of the regression function. The results of numerical simulation as well as the IBM stock data analysis indicate that the method is effective.