NSD样本最近邻密度估计的强相合性  

Strong Consistency of Nearest Neighbor Estimator of Density Function for NSD Sequences

作　　者：聂彩玲 李永明[2,3] 应锐 NIE Cailing;LI Yongming;YING Rui(College of Sciences, Nanchang University, Nangchang 330031, China;School of Mathematics and Computer Science, Shangrao Normal University, Shangrao 334001,China;School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai 200433, China;Shangrao Normal School, Shangrao 334001,China)

机构地区：[1]南昌大学理学院,江西南昌330031 [2]上饶师范学院数学与计算机科学学院,江西上饶334001 [3]上海财经大学统计与管理学院,上海200433 [4]上饶师范学校,江西上饶334001

出　　处：《应用数学》2019年第4期865-871,共7页Mathematica Applicata

基　　金：国家自然科学基金资助项目(11461057,11561010);国家自然科学基金委重点项目(71331006)

摘　　要：本文研究负超可加相依样本的最近邻密度估计强相合性.利用负超可加相依序列的不等式与性质,获得最近邻密度估计的弱相合性、强相合性和一致强相合性.In this paper, we study strong consistency of the nearest neighbor density estimator for NSD samples. By using the inequality and property of NSD, we obtian the weak consistency , strong consistency and uniformly strong consistency of the nearest neighbor estimator for unknown probability density function.

关 键 词：负超可加相依 最近邻密度估计 强相合性 

分 类 号：O211.67[理学—概率论与数理统计]