LNQD样本最近邻密度估计的相合性Consistency of Nearest Neighbor Estimation of Density Function for Linearly Negative Quadrant Dependent Samples
崔永君;杨善朝;梁丹;
摘要(Abstract):
本文在LNQD样本下研究最近邻密度估计的相合性,给出弱相合性、强相合性、一致强相合性以及它们的收敛速度的充分条件,同时研究了失效率函数估计的一致强相合性。
关键词(KeyWords): LNQD序列;最近邻密度估计;相合性
基金项目(Foundation): 国家自然科学基金资助项目(11061007);; 广西自然科学基金资助项目(2011GXNSFA018133)
作者(Authors): 崔永君;杨善朝;梁丹;
DOI: 10.16088/j.issn.1001-6600.2012.02.023
参考文献(References):
- [1]LEHMANN E L.Some concepts of dependence[J].The Annals of Mathematical Statistics,1966,37(5):1137-1153.
- [2]NEWMAN C M.Asymptotie independence and limit theorems for positively and negatively dependent random vari-ables[C]//TONG Y L.Proceedings of the Symposium on Inequalities in Statisties and Probabilit.Hayward,CA:Insti-tute of Mathematical Statistics,1984:127-140.
- [3]LOFTSGAARDEN D O,QUESENBERRY C P.A nonparametric estimate of a multivariate density function[J].An-nals of Mathematical Statistics,1965,36(3):1049-1051.
- [4]王学军.弱鞅和三类相依序列的概率不等式及极限定理[D].安徽:安徽大学,2010:61-78.
- [5]WANG Jian-feng,ZHANG Li-xin.A Berry-Esseen theorem for weakly negatively dependent random variables and itsapplications[J].Acta Math Hungar,2006,110(4):293-308.
- [6]KO M H,CHOI Y K,CHOI Y S.Exponential probability inequality for linearly negative quadrant dependent randomvariables[J].Communications Korean Mathmatical Society,2007,22(1):137-143.
- [7]KO Mi-hwa,RYU Dae-hee,KIM Tae-sun.Limiting behaviors of weighted sums for linearly negative quadrant depen-dent random variables[J].Taiwanese Journal of Mathematics,2007,11(2):511-512.
- [8]MOORE D S,YACKEL J W.Large sample properties of nearest neighbor density function estimators[M].StatisticalDecision Theory and Related Topics.New York:Academic Press,1977.
- [9]DEVROYE L P,WAGNER T J.The strong uniform consistency of nearest neighbor density function estimators[J].Ann Statist,1977,5(3):536-540.
- [10]陈希孺.最近邻密度估计的收敛速度[J].中国科学,1981(12):1419-1428.
- [11]BOENTE G,FRAIMAN R.Consistency of a nonparametric estimate of a density function for dependent variables[J].J Multivariate Analysis,1988,25(1):90-99.
- [12]柴根象.平稳序列最近邻密度估计的相合性[J].数学学报,1989,32(3):423-432.
- [13]杨善朝.NA样本最近邻密度估计的相合性[J].应用数学学报,2003,26(3):385-394.
- [14]刘妍岩,张艳丽.NQD样本最近邻密度估计的相合性[J].武汉大学学报:理学版,2006,52(1):13-16.
- [15]凌能祥,许昌满,彭小智.NQD样本下密度函数核估计的相合性[J].合肥工业大学学报:自然科学版,2008,31(2):287-290.