本文關(guān)鍵詞： M估計 遍歷數(shù)據(jù) 幾乎完全收斂 漸近正態(tài)性 收斂速度　出處：《合肥工業(yè)大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：作為統(tǒng)計中熱門的領(lǐng)域,非參數(shù)估計常常面臨異常值存在或者殘差重尾分布的情況。因此,能減弱估計值不夠穩(wěn)健的M估計方法具有著重要的研究意義,其相關(guān)結(jié)果也備受學(xué)者們的關(guān)注。實際研究中數(shù)據(jù)獨立的情況很少,盡管?-混合是常見的混合條件中最弱的,然而要驗證非線性時間序列是否符合?-混合條件卻很有難度。因此,研究不需要許多條件驗證且能包含?-混合不能全部包含的相依結(jié)構(gòu)的遍歷性數(shù)據(jù)是很有必要的。近年來,一些學(xué)者建立了改良的M估計方法,目的是在M估計原有的優(yōu)勢上吸收其他估計量的長處。本文采用遞歸的M估計方法,研究了平穩(wěn)遍歷條件下函數(shù)型數(shù)據(jù)非參數(shù)穩(wěn)健估計的收斂速度以及漸近性質(zhì)。主要內(nèi)容如下:1.給出平穩(wěn)遍歷函數(shù)型非參數(shù)遞歸M估計的收斂速度:基于平穩(wěn)遍歷函數(shù)型數(shù)據(jù),構(gòu)造函數(shù)型非參數(shù)回歸函數(shù)的遞歸M估計量,利用一些合理的正則條件證明非參數(shù)遞歸M回歸估計的幾乎完全一致收斂并給出收斂速度。推廣了現(xiàn)有文獻(xiàn)中的相關(guān)的結(jié)果。2.給出平穩(wěn)遍歷函數(shù)型非參數(shù)M估計/遞歸M估計的漸近分布:基于平穩(wěn)遍歷函數(shù)型數(shù)據(jù),分別給出不同的正則條件,通過合理的推導(dǎo)證明非參數(shù)M回歸估計的漸近正態(tài)性和非參數(shù)遞歸M回歸估計的漸近正態(tài)性。推廣了現(xiàn)有文獻(xiàn)中的相關(guān)結(jié)果。
[Abstract]:As a popular field in statistics, nonparametric estimation is often faced with the existence of outliers or the residual heavy-tailed distribution. Therefore, it is of great significance to study the M estimation method, which can weaken the estimation value and is not robust enough. The related results have attracted the attention of scholars. There are few cases of data independence in practical research, although? -mixing is the weakest of the common mixing conditions, however, to verify whether nonlinear time series match? -mixing conditions are difficult. Therefore, the study does not require a lot of conditional verification and can include? -it is necessary to mix ergodicity data of dependent structures which can not be completely contained. In recent years, some scholars have established an improved M-estimation method. The purpose of this paper is to absorb the advantages of other estimators on the advantage of M estimation. The convergence rate and asymptotic property of nonparametric robust estimation of functional data under stationary ergodic condition are studied. The main contents are as follows: 1. The convergence rate of nonparametric recursive M estimator of stationary ergodic function type is given: based on stationary ergodic function data, Recursive M estimators of nonparametric regression functions of constructor type, Using some reasonable regular conditions, the almost uniform convergence of nonparametric recurrent M regression estimation is proved and the convergence rate is given. The related results. 2. The nonparametric M estimator of stationary ergodic function is given. Asymptotic distribution of / recursive M estimator: based on stationary ergodic function data, The asymptotic normality of nonparametric M regression estimation and the asymptotic normality of nonparametric recurrent M regression estimation are proved by reasonable derivation of different regular conditions.
【學(xué)位授予單位】：合肥工業(yè)大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O212.1

【相似文獻(xiàn)】

相關(guān)期刊論文 前3條

1 莊常陵;;M估計存在的條件[J];長春師范學(xué)院學(xué)報;2005年12期

2 陳鑫;伍艷春;;誤差為ρ~-時非線性模型M估計的強(qiáng)相合性[J];重慶文理學(xué)院學(xué)報(自然科學(xué)版);2010年03期

3 包鑫;戴連奎;;基于M估計器的支持向量機(jī)算法及其應(yīng)用[J];化工學(xué)報;2009年07期

相關(guān)碩士學(xué)位論文 前2條

1 陳楚曦;基于平穩(wěn)遍歷函數(shù)型非參數(shù)遞歸M估計[D];合肥工業(yè)大學(xué);2017年

2 肖麗華;相依樣本線性模型參數(shù)M估計的強(qiáng)相合性[D];廣西師范大學(xué);2002年

，

本文編號：1525902