两类相依样本下密度函数估计的相合性

发布时间：2019-01-04 12:24

【摘要】：由于宽象限相依(WOD)是一类包括扩展负相依(END)、负相依(ND)、负相关(NA)在内更普遍的相依随机变量序列,并且广泛地应用于风险分析、多元分析、可靠性理论等多个领域.故将独立或者其它相依序列的非参数统计大样本性质推广到WOD、END情形下是非常重要的.本文主要讨论了WOD、END随机变量样本序列未知密度函数的最近邻密度估计与核密度估计的一些大样本性质,如强相合性、一致强相合性、强收敛速度,同时,也讨论了失效率函数的强收敛速度.推广了独立和其它相依随机变量样本序列下相应的密度函数估计量的大样本性质.全文共分四章.第一章:概述未知密度函数估计问题的研究背景及方法,随机变量序列WOD、END的国内外研究现状并给出了本文的主要研究结果.第二章:由END随机变量样本序列的Bernstein不等式、Rosenthal不等式,在.适当的前提下得到了END随机变量样本序列密度函数递归核估计量的强相合性及r阶矩相合性.第三章:由WOD随机变量样本序列的Exponential不等式,在适当的前提下得到了 WOD随机变量样本序列密度函数一般核估计量的一致强相合性、均方相合性及强收敛速度,同时,作为应用也讨论了失效率函数的强收敛速度.第四章:由WOD随机变量样本序列的Bernstein不等式,在适当的假设前提下得到了 WOD随机变量样本序列未知密度函数最近邻密度估计的一致强相合收敛速度.
[Abstract]:Because wide quadrant dependent (WOD) is a more common sequence of dependent random variables including extended negative dependent (END), negatively dependent (ND), negatively correlated (NA), it is widely used in risk analysis and multivariate analysis. Reliability theory and other fields. Therefore, it is very important to extend the nonparametric statistical large sample properties of independent or other dependent sequences to the WOD,END case. In this paper, we mainly discuss some large sample properties of the nearest neighbor density estimation and kernel density estimation for the unknown density function of the sample sequence of WOD,END random variables, such as strong consistency, uniform strong consistency, strong convergence rate, at the same time, The strong convergence rate of failure rate function is also discussed. The large sample properties of the corresponding density function estimators for independent and other dependent random variable sample sequences are generalized. The full text is divided into four chapters. Chapter 1: the research background and methods of unknown density function estimation are summarized. The research status of random variable sequence WOD,END at home and abroad and the main results of this paper are given. Chapter 2: Bernstein inequality and Rosenthal inequality of END random variable sample sequence. The strong consistency and r order moment consistency of the recursive kernel estimators for the density function of END random variables are obtained. Chapter 3: from the Exponential inequality of the sample sequence of WOD random variable, we obtain the uniform strong consistency, mean square consistency and strong convergence rate of the kernel estimator of the density function of the sample sequence of WOD random variable under the appropriate premise, at the same time, The strong convergence rate of the failure rate function is also discussed as an application. Chapter 4: based on the Bernstein inequality of the sample sequence of WOD random variables, the uniformly strongly consistent convergence rate of the nearest neighbor density estimation of the unknown density function of the sample sequence of WOD random variables is obtained under appropriate assumptions.
【学位授予单位】：广西师范学院
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212

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