The Convergence Properties Of Kernel Density Estimation Under Censored Data

As is known to all, kernel density estimation is widely used in the field of a nonparametric statistical method. Ever since Rosenblatt and Parzen put forward the density estimation, many scholars at home and abroad study the theory of probability and mathematical statistics and achieved many significant results. Under the censored data, however, the study of large sample properties of the kernel density estimation of dependent variable is relatively rare. Thus to study large sample properties of kernel density estimation in censored data is full of great theoretical significance.In this paper, I dedicate to study large sample properties of kernel density estimation in censored data. I achieve some convergence properties in α-mixing and NA sample kernel density estimation of censored data as point by point strong consistency, uniform strong consistency, point by point consistency speed, strong consistency speed and asymptotic normality to spread large sample properties in dependent and some other dependent case of censored data. The main studies content as below.In chapter one, I introduce the research background and the selected topic significance of kernel density estimation and α-mixing and NA series. And the dependent variable of kernel density estimation and delete kernel density estimation under the censored data of consistency and gradual convergence properties of normality at home and abroad to under. Finally, the main research results of this paper is given.In chapter two, in the condition of the density function f(x) and kernel function K(·)meeting the Lipschitz, I study the point by point strong consistency and uniform Strong Consistency of censored data in α-mixing series of certain conditions based on the index inequality of α-mixing series and some properties of α-mixing x series.In chapter three, in the condition of the density function f(x) and kernel function K()meeting the Lipschitz and the second derivative f"(x)is bounded, I study point by point strong consistency speed and uniform Strong Consistency speed of censored data in α-mixing series of certain conditions based on the index inequality of α-mixing and some properties of α-mixing. Their speed is respectively andIn chapter four, I study point by point strong consistency and uniform Strong Consistency of kernel density estimation of censored data in NA sample based on moment inequalities and bounded variation of NA series.In chapter five, I study asymptotic normality of censored data in NA sample based on principles such as the central limit theorem and blocking.