本文選題：經(jīng)驗(yàn)似然 + 漸近正態(tài)　； 參考：《中國(guó)礦業(yè)大學(xué)》2015年碩士論文

【摘要】：經(jīng)驗(yàn)似然方法是由Owen提出的一種非參數(shù)統(tǒng)計(jì)推斷方法,具有良好的漸近性質(zhì),如何將這種方法用于部分線性ARCH誤差模型的統(tǒng)計(jì)推斷是一個(gè)熱點(diǎn)的問題.雖然文獻(xiàn)中利用最大似然估計(jì)的方法構(gòu)造了經(jīng)驗(yàn)似然統(tǒng)計(jì)量,但要求誤差項(xiàng)的四階矩有限,這個(gè)要求一般對(duì)金融時(shí)間序列過于苛刻.因此,本文利用最小絕對(duì)偏差(LAD)估計(jì)方法構(gòu)造經(jīng)驗(yàn)似然統(tǒng)計(jì)量,在誤差項(xiàng)是厚尾分布的情況下,分別推導(dǎo)出LAD估計(jì)量和經(jīng)驗(yàn)似然比統(tǒng)計(jì)量的漸近性質(zhì).最后,本文進(jìn)行了蒙特卡羅模擬,模擬出這兩種方法的置信區(qū)域的覆蓋率,根據(jù)模擬所得到的結(jié)果比較了這兩種方法的優(yōu)越性.具體做了以下幾個(gè)方面的工作:第一,對(duì)部分線性ARCH誤差模型,構(gòu)造參數(shù)的目標(biāo)函數(shù),然后求目標(biāo)函數(shù)的最小值,得到LAD估計(jì)量;第二,根據(jù)鞅的中心極限定理和遍歷性定理,證明了LAD估計(jì)量的漸近正態(tài)性,并且給出了漸近正態(tài)置信區(qū)域;第三,在LAD估計(jì)的基礎(chǔ)上,構(gòu)造了經(jīng)驗(yàn)似然比統(tǒng)計(jì)量,然后了證明經(jīng)驗(yàn)似然比統(tǒng)計(jì)量的漸近性質(zhì),并且給出了經(jīng)驗(yàn)似然置信區(qū)域;第四,進(jìn)行數(shù)據(jù)模擬,計(jì)算置信區(qū)域的覆蓋率,通過進(jìn)行對(duì)比,得出經(jīng)驗(yàn)似然方法具有更好的優(yōu)越性.
[Abstract]:Empirical likelihood method is a nonparametric statistical inference method proposed by Owen. It has good asymptotic property. How to apply this method to the statistical inference of partial linear ARCH error model is a hot issue. Although the empirical likelihood statistics are constructed by using the method of maximum likelihood estimation in the literature, the fourth order moment of the error term is limited, which is generally too harsh for the financial time series. In this paper, the empirical likelihood statistics are constructed by using the method of minimum absolute deviation (lad) estimation. The asymptotic properties of the LAD estimator and the empirical likelihood ratio statistic are derived under the condition that the error term is a thick-tailed distribution. Finally, Monte Carlo simulation is carried out to simulate the confidence region coverage of the two methods, and the advantages of the two methods are compared according to the simulation results. The main work is as follows: firstly, the objective function of parameter is constructed for partial linear ARCH error model, then the minimum value of objective function is obtained, and the LAD estimator is obtained. Secondly, according to the central limit theorem and ergodicity theorem of martingale, The asymptotic normality of LAD estimator is proved, and the asymptotic normal confidence region is given. Thirdly, on the basis of LAD estimation, empirical likelihood ratio statistics are constructed, and the asymptotic properties of empirical likelihood ratio statistics are proved. And the empirical likelihood confidence region is given. Fourth, the data simulation, the calculation of confidence region coverage, through comparison, it is concluded that empirical likelihood method has better advantages.
【學(xué)位授予單位】：中國(guó)礦業(yè)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類號(hào)】：O212.1

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本文編號(hào)：1897591