Nonparametric Model Change Point Detection And Delete Data Loss In Delete Loss Index Under The Random Missing Estimate Of Regression Function

The change point problem is one of the hot topics in statistical research. Change point detection is not only widely used in the industrial field of quality control, but also used in the financial, economic, medical, computer and other fields. In this paper, wavelet methods are adopted to study the detection and estimation of change points in variance models and hazard rate models.Firstly, in chapter II, we study the detection and estimation of change points in volatility under nonparametric regression models with a-mixing observations. Wavelet methods are applied to construct the test statistic to detect change points in volatility. The asymptotic distribution of the test statistic is established. We also utilize the test statistic to construct the estimators for the number, locations, and jump sizes of the change points in volatility. The asymptotic properties of these estimators are derived. Some simulation studies are conducted to assess the finite sample performances of the proposed procedures.In Chapter III, we study the detection and estimation of change points in hazard rate models with censored data. Wavelet methods are used to construct test statistic. The asymptotic distribution of the test statistic is explored. We also propose estimators for the number, locations, and jump sizes of the change points in hazard rate. The asymptotic properties of these estimators are derived. Some simulation examples are conducted to assess the finite sample performances of our methods and a real data example is provided.In Chapter IV, we extend our methods to the case that the censored ob-servations are a-mixing. The asymptotic properties of the test statistic and the estimators are established. Some simulation examples are conducted to assess the finite sample performances of our methods in α-mixing censored case.Finally, In Chapter V, we consider the estimation of regression function when the censoring indicator is missing at random. We use nonpar ametric technique and inverse probability weighted method to define two kernel estimators for the regression function. We establish the strong uniform convergence with rates and the asymptotic normality of our estimators. Some simulations are conducted to assess the finite sample performances of our methods.