Two Kinds Of Data Semiparametric Regression Model Estimation Theory

The semi-parametric regression model is an important statistical model which develops from late 80s. Since it contains not only a parametric component but also a non- parametric component, and can be used to describe many actual problems, the model is widely paid attention to.In practice (survival analysis, reliability of life experiment, medicine pursuing experiment), there are different kinds of incomplete data, censored data and contaminated data are among them. So it becomes very necessary to investigate the model under such data. In this paper, some large sample propositions of the model under these two kinds of data are obtained. The main contents are as follows:1. For the model under random censorship, when the distribution of the censored data is consistent and known, the M-estimators are studied. Under some mild conditions, the rates of convergence and the asymptotic normality of the unknown parameter are obtained.2. For the model under random censorship, when the distribution of the censored data is consistent but unknown, the M-estimators are studied. Under some mild conditions, the rates of convergence and asymptotic normality of the M-estimators are obtained.3. For the model under contaminated data, the methods of least-squares estimation and random weighting are proposed to obtain the estimators of β,g and thecontaminated parameter. Under some mild conditions, their consistency is proved.