【摘要】：已有大量數(shù)據(jù)表明,金融、保險(xiǎn)、網(wǎng)絡(luò)、生物學(xué)以及風(fēng)險(xiǎn)理論等領(lǐng)域的時(shí)間序列數(shù)據(jù)并不滿足正態(tài)分布,而是展現(xiàn)出尖峰厚尾的特征。為此,對(duì)重尾分布及尾指數(shù)估計(jì)的研究顯得十分重要,如何對(duì)尾指數(shù)做出無偏且穩(wěn)健的估計(jì)成為學(xué)者們關(guān)注的熱點(diǎn)。本文首先介紹了極值理論和正則變化條件。其次,介紹了 MOP估計(jì)在一階條件下的一致性與二階條件下的漸近正態(tài)性,并且假設(shè)在較強(qiáng)的三階條件下證明了MOP估計(jì)的漸近展開式,相比于較弱二階條件下的結(jié)論得到關(guān)于漸近偏差的更多信息。然后,介紹了OMOP估計(jì)和ORBMOP估計(jì),并在三階條件下證明了 ORBMOP估計(jì)的漸近展開式和漸近正態(tài)性且在一定條件下獲得了一個(gè)非零漸近偏差。在保證方差為γ2(1-φρ)2/(1-2φρ)的前提下,提出ORBMOP的一種修正估計(jì)(?)*(κ)并在三階條件下證明了它的漸近正態(tài)性,當(dāng)γ 0或γ 0時(shí)比較了二者的漸近偏差。最后,在有限樣本情形下,利用三種常見重尾模型對(duì)本文提出的(?)*(κ)估計(jì)與ORBMOP估計(jì)和經(jīng)典降偏差CH估計(jì)進(jìn)行Monte-Carlo模擬比較,模擬均值表明(?)*(κ)估計(jì)比ORBMOP和CH更接近γ真值,模擬均方誤差表明(?)*(κ)估計(jì)的均方誤差更小。因此,本文提出的修正的降偏差估計(jì)(?)*(κ)表現(xiàn)更好。
[Abstract]:A large number of data have shown that the time series data in the fields of finance, insurance, network, biology and risk theory do not satisfy the normal distribution, but show the characteristics of peak and thick tail. Therefore, it is very important to study the heavy-tailed distribution and tail index estimation. How to estimate the tail index unbiased and robust has become a hot topic. In this paper, the extreme value theory and the regular variation conditions are introduced. Secondly, we introduce the consistency of MOP estimator under the first order condition and the asymptotic normality under the second order condition, and prove the asymptotic expansion of the MOP estimate under the strong third order condition. More information about the asymptotic deviation is obtained than that under the weaker second order condition. Then, the OMOP and ORBMOP estimators are introduced, and the asymptotic expansions and asymptotic normality of ORBMOP estimators are proved under the third-order conditions, and a nonzero asymptotic deviation is obtained under certain conditions. Under the condition that the variance is 緯 2 (1- 蠁 蟻) 2 / (1-2 蠁 蟻), a modified estimate of ORBMOP (?) * (魏) is proposed and its asymptotic normality is proved under the third-order condition. The asymptotic deviations are compared when 緯 0 or 緯 0. Finally, in the case of limited samples, three kinds of common heavy-tailed models are used to compare the (?) * (魏) estimators proposed in this paper with ORBMOP estimators and classical reduced deviation CH estimators. The simulated mean value shows that (?) * (魏) estimation is closer to 緯 true value than ORBMOP and CH, and the simulated mean square error indicates that the mean square error of (?) * (魏) estimation is smaller than that of ORBMOP and CH. Therefore, the revised reduced deviation estimate (?) * (魏) proposed in this paper performs better.
【學(xué)位授予單位】：山西大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O212.1

【參考文獻(xiàn)】

相關(guān)期刊論文 前2條

1 劉維奇;赫英迪;陳琳;;重尾分布的尾部指數(shù)估計(jì)及滬深股市實(shí)證分析[J];數(shù)學(xué)的實(shí)踐與認(rèn)識(shí);2011年06期

2 劉維奇;邢紅衛(wèi);;重尾指數(shù)估計(jì)中閾值k的簡便優(yōu)化估計(jì)[J];系統(tǒng)工程理論與實(shí)踐;2010年08期

相關(guān)碩士學(xué)位論文 前1條

1 邢紅衛(wèi);重尾現(xiàn)象、重尾分布與重尾指數(shù)估計(jì)[D];山西大學(xué);2010年

，

本文編號(hào)：2399695