Generalized Consistency For Kernel Density Estimation

This thesis studies several kinds of consistency for kernel density estimation under X1,X2,…,Xn are independent and identically distributed (iid).In the first chapter, we mainly introduce main study results of the kernel density estimation at present, and also introduce the concern knowledge and study method of kernel density estimation. Finally, the main work of this thesis are given.In the second chapter, we define the Pearson-χ2 distance and Kullback-Leibler distance between two random density functions, and then discuss the two distances of some ordinary distributions. At the end of this chapter,we study the Pearson-χ2 distance and Kullback-Leibler distance of order statistics.In the third chapter, we introduce the definition of kernel density estimation under X1,X2,…,Xn are independent and identically distributed (iid).In order to discuss generalized consistency for kernel density estimation, some important lemmas are given to supply its theorem basis.In the fourth chapter, first of all, we study the consistency of r-power (0