本文選題：經(jīng)驗(yàn)似然　切入點(diǎn)：鞅差誤差　出處：《安徽工程大學(xué)》2017年碩士論文　論文類(lèi)型：學(xué)位論文

【摘要】：Owen(1988)提出的經(jīng)驗(yàn)似然(Empirical Likelihood,EL)是一個(gè)有影響力的計(jì)算密集型數(shù)據(jù)的統(tǒng)計(jì)方法。此方法定義了一個(gè)經(jīng)驗(yàn)似然比函數(shù),并使用受約束參數(shù)影響的其最大值來(lái)構(gòu)建置信區(qū)間/區(qū)域。作為某種意義上分布假設(shè)自由的一種非參數(shù)似然方法,經(jīng)驗(yàn)似然在推導(dǎo)未知參數(shù)的置信區(qū)間方面有許多突出的優(yōu)點(diǎn)。例如,經(jīng)驗(yàn)似然推理不涉及方差估計(jì),基于經(jīng)驗(yàn)似然的置信區(qū)域形狀和方向完全由數(shù)據(jù)本身決定,等等。正因?yàn)槿绱?經(jīng)驗(yàn)似然方法引起了許多統(tǒng)計(jì)學(xué)者的興趣,他們將這一方法應(yīng)用到各種統(tǒng)計(jì)模型及各種領(lǐng)域。本文的主要內(nèi)容是研究基于半?yún)?shù)回歸模型參數(shù)的經(jīng)驗(yàn)似然問(wèn)題。首先,我們研究在鞅差誤差下高維部分線(xiàn)性模型參數(shù)的經(jīng)驗(yàn)似然。在誤差是相依情形,即誤差是鞅差誤差時(shí),給出相應(yīng)的經(jīng)驗(yàn)似然比檢驗(yàn)統(tǒng)計(jì)量,以及滿(mǎn)足的漸近性質(zhì),并考慮模型參數(shù)的線(xiàn)性組合情形,然后通過(guò)一些基本條件以及一些引理證明漸近性質(zhì),并利用MATLAB數(shù)據(jù)模擬,說(shuō)明經(jīng)驗(yàn)似然方法比profile最小二乘表現(xiàn)效果好。其次,在鞅差誤差下考慮部分函數(shù)線(xiàn)性模型參數(shù)的經(jīng)驗(yàn)似然。通過(guò)Mercer's定理和Karhunen-Loeve表達(dá)式推導(dǎo)出部分函數(shù)線(xiàn)性模型的近似表達(dá)式,給出相應(yīng)的經(jīng)驗(yàn)似然比檢驗(yàn)統(tǒng)計(jì)量,以及滿(mǎn)足的漸近性質(zhì),通過(guò)一些基本條件以及一些引理證明該漸近性質(zhì)。最后,我們考慮高維部分函數(shù)線(xiàn)性模型的經(jīng)驗(yàn)似然。給出相應(yīng)的經(jīng)驗(yàn)似然比檢驗(yàn)統(tǒng)計(jì)量,以及滿(mǎn)足的漸近性質(zhì),通過(guò)一些基本條件以及一些引理證明該漸近性質(zhì),并利用MATLAB數(shù)據(jù)模擬,說(shuō)明經(jīng)驗(yàn)似然方法比profile最小二乘表現(xiàn)效果好。
[Abstract]:The empirical likelihood likelihood (ELL) is an influential statistical method for computationally intensive data, which defines an empirical likelihood ratio function. The confidence interval / region is constructed by using the maximum value affected by constrained parameters, which is a nonparametric likelihood method for the freedom of distribution assumption in a sense. Empirical likelihood has many outstanding advantages in deriving confidence intervals of unknown parameters. For example, empirical likelihood reasoning does not involve variance estimation, and the shape and direction of confidence regions based on empirical likelihood are entirely determined by the data itself. And so on. Because of this, the empirical likelihood method has attracted the interest of many statisticians, They apply this method to various statistical models and fields. The main content of this paper is to study the empirical likelihood problem based on semi-parametric regression model parameters. In this paper, we study the empirical likelihood of parameters of high dimensional partial linear model under martingale error. When the error is dependent, that is, the error is martingale difference error, the empirical likelihood ratio test statistic is given, and the asymptotic property is obtained. Considering the linear combination of the model parameters, the asymptotic properties are proved by some basic conditions and some Lemma, and the simulation results of MATLAB data show that the empirical likelihood method is better than the profile least squares representation. Secondly, The empirical likelihood of parameters of partial function linear model is considered under martingale error. The approximate expression of partial function linear model is derived by Mercer's theorem and Karhunen-Loeve expression, and the corresponding empirical likelihood ratio test statistic is given. The asymptotic property is proved by some basic conditions and some Lemma. Finally, we consider the empirical likelihood of the linear model of high dimensional partial function, and give the corresponding empirical likelihood ratio test statistic. The asymptotic property is proved by some basic conditions and some Lemma, and the simulation of MATLAB data shows that the empirical likelihood method is better than the profile least square method.
【學(xué)位授予單位】：安徽工程大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類(lèi)號(hào)】：O212.1

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