發(fā)布時間：2019-01-04 12:24

【摘要】：由于寬象限相依(WOD)是一類包括擴展負相依(END)、負相依(ND)、負相關(guān)(NA)在內(nèi)更普遍的相依隨機變量序列,并且廣泛地應用于風險分析、多元分析、可靠性理論等多個領(lǐng)域.故將獨立或者其它相依序列的非參數(shù)統(tǒng)計大樣本性質(zhì)推廣到WOD、END情形下是非常重要的.本文主要討論了WOD、END隨機變量樣本序列未知密度函數(shù)的最近鄰密度估計與核密度估計的一些大樣本性質(zhì),如強相合性、一致強相合性、強收斂速度,同時,也討論了失效率函數(shù)的強收斂速度.推廣了獨立和其它相依隨機變量樣本序列下相應的密度函數(shù)估計量的大樣本性質(zhì).全文共分四章.第一章:概述未知密度函數(shù)估計問題的研究背景及方法,隨機變量序列WOD、END的國內(nèi)外研究現(xiàn)狀并給出了本文的主要研究結(jié)果.第二章:由END隨機變量樣本序列的Bernstein不等式、Rosenthal不等式,在.適當?shù)那疤嵯碌玫搅薊ND隨機變量樣本序列密度函數(shù)遞歸核估計量的強相合性及r階矩相合性.第三章:由WOD隨機變量樣本序列的Exponential不等式,在適當?shù)那疤嵯碌玫搅?WOD隨機變量樣本序列密度函數(shù)一般核估計量的一致強相合性、均方相合性及強收斂速度,同時,作為應用也討論了失效率函數(shù)的強收斂速度.第四章:由WOD隨機變量樣本序列的Bernstein不等式,在適當?shù)募僭O前提下得到了 WOD隨機變量樣本序列未知密度函數(shù)最近鄰密度估計的一致強相合收斂速度.
[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.
【學位授予單位】：廣西師范學院
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O212

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