The Asymptotic Property Of Nearest-Neighbor Density Estimator

This dissertation is concerned with some problems regarding the asymptotic property of nearest-neighbor density(NN) estimator for α—mixing and nagetive quadrant dependent (NQD) samples. The results extend the corresponding theorems in i.i.d. case.This dissertation is devided into three parts .In chapter one, we introduced some background material and research results that have obtained of the nearest neighbor density estimator .In chapter two we investigated the consistency and asymptotic normality property of NN-estimator under α-mixing condition.In chapter three, we first introduced the Marcinkiewicz large law and Bernstein inequality, then we gave the sufficent conditions for weak consistency, strong consistency and uniformly strong consistency of NN-estimator for NQD samples.