【作者】 许昌满；

【导师】 凌能祥；

【作者基本信息】 合肥工业大学 ， 应用数学， 2008， 硕士

【摘要】 本文主要研究了基于两两NQD样本的密度函数估计问题,得到了两两NQD样本下最近邻估计和核估计的大样本性质,如相合性、渐近正态性及收敛速度等。从而推广了独立同分布和其它相依情形下的相关结果。全文共分四部分。第一部分介绍了密度函数估计的背景、意义、方法及本文的主要成果。第二部分介绍了基于两两NQD样本最近邻密度估计的相合性并讨论了它们的收敛速度。第三部分重点讨论了基于两两NQD样本密度函数核估计的强相合、一致强相合及r-阶矩相合。第四部分讨论了基于两两NQD样本密度函数核估计的渐近正态性。更多还原

【Abstract】 This paper is mainly concerned with the density function estimation problems under pairwises NQD samples, based on which we got the consistency, asymptotic property as well as the consistency rates and other large sample properties of the nearest neighbor estimation and kernel estimation. All the studies together have promoted the concerned results in i.i.d case and other associationsThis paper consists of four parts.In the first section, we introduced some background information, significance, the way of density function estimation and the chief results of this paper.In the second section, we introduced the consistency of nearest neighbor density estimation under pairwises NQD samples. In addition, we also discussed its consistency rates.In the third section, we focused our attention on the density kernel estimation under pairwises NQD samples and mainly talked about its strong consistency, uniformly strong consistency and the consistency in r-th order mean.In the last section, we investigated the asymptotic normality of density function kernel estimation under pairwises NQD samples.更多还原