【摘要】：由于寬象限相依(WOD)是一類包括擴(kuò)展負(fù)相依(END)、負(fù)相依(ND)、負(fù)相關(guān)(NA)在內(nèi)更普遍的相依隨機(jī)變量序列,并且廣泛地應(yīng)用于風(fēng)險(xiǎn)分析、多元分析、可靠性理論等多個(gè)領(lǐng)域.故將獨(dú)立或者其它相依序列的非參數(shù)統(tǒng)計(jì)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(jī)變量樣本序列未知密度函數(shù)的最近鄰密度估計(jì)與核密度估計(jì)的一些大樣本性質(zhì),如強(qiáng)相合性、一致強(qiáng)相合性、強(qiáng)收斂速度,同時(shí),也討論了失效率函數(shù)的強(qiáng)收斂速度.推廣了獨(dú)立和其它相依隨機(jī)變量樣本序列下相應(yīng)的密度函數(shù)估計(jì)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(jì)問(wèn)題的研究背景及方法,隨機(jī)變量序列WOD、END的國(guó)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(jī)變量樣本序列的Bernstein不等式、Rosenthal不等式,在.適當(dāng)?shù)那疤嵯碌玫搅薊ND隨機(jī)變量樣本序列密度函數(shù)遞歸核估計(jì)量的強(qiáng)相合性及r階矩相合性.第三章:由WOD隨機(jī)變量樣本序列的Exponential不等式,在適當(dāng)?shù)那疤嵯碌玫搅?WOD隨機(jī)變量樣本序列密度函數(shù)一般核估計(jì)量的一致強(qiáng)相合性、均方相合性及強(qiáng)收斂速度,同時(shí),作為應(yīng)用也討論了失效率函數(shù)的強(qiáng)收斂速度.第四章:由WOD隨機(jī)變量樣本序列的Bernstein不等式,在適當(dāng)?shù)募僭O(shè)前提下得到了 WOD隨機(jī)變量樣本序列未知密度函數(shù)最近鄰密度估計(jì)的一致強(qiáng)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(xué)位授予單位】：廣西師范學(xué)院
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O212

【參考文獻(xiàn)】

相關(guān)期刊論文 前10條

1 胡學(xué)平;張紅梅;;WOD樣本下密度函數(shù)核估計(jì)的收斂性[J];山東大學(xué)學(xué)報(bào)(理學(xué)版);2017年04期

2 秦永松;雷慶祝;;強(qiáng)混合樣本下最近鄰密度估計(jì)的漸近正態(tài)性[J];數(shù)學(xué)年刊A輯(中文版);2016年04期

3 李永明;應(yīng)銳;蔡際盼;姚竟;;WOD樣本密度函數(shù)和失效率函數(shù)遞歸核估計(jì)的逐點(diǎn)強(qiáng)相合性[J];吉林大學(xué)學(xué)報(bào)(理學(xué)版);2015年06期

4 劉振;吳群英;葉彩園;;WOD樣本最近鄰密度估計(jì)的相合性[J];桂林理工大學(xué)學(xué)報(bào);2014年04期

5 Dehua QIU;Tienchung HU;;Strong Limit Theorems for Weighted Sums of Widely Orthant Dependent Random Variables[J];Journal of Mathematical Research with Applications;2014年01期

6 施生塔;吳群英;;WOD樣本下密度函數(shù)核估計(jì)的強(qiáng)相合性[J];浙江大學(xué)學(xué)報(bào)(理學(xué)版);2014年01期

7 蘭沖鋒;;NQD樣本最近鄰密度估計(jì)的一致強(qiáng)相合速度[J];阜陽(yáng)師范學(xué)院學(xué)報(bào)(自然科學(xué)版);2013年04期

8 劉振;吳群英;葉彩園;;刪失樣本α混合序列遞歸核密度估計(jì)的一致強(qiáng)相合性及速度[J];湖北大學(xué)學(xué)報(bào)(自然科學(xué)版);2013年04期

9 陳志勇;劉婷婷;陳燭薔;王學(xué)軍;;AANA序列的強(qiáng)大數(shù)定律和強(qiáng)收斂速度[J];合肥工業(yè)大學(xué)學(xué)報(bào)(自然科學(xué)版);2012年12期

10 劉艷;吳群英;;ND樣本最近鄰密度估計(jì)的一致強(qiáng)相合性[J];華僑大學(xué)學(xué)報(bào)(自然科學(xué)版);2012年05期

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