本文選題：極大似然估計 + 大樣本性質(zhì)　； 參考：《海南師范大學(xué)》2017年碩士論文

【摘要】：Quantile第Ⅰ類分布是一類為克服經(jīng)典分布在擬合金融收益率數(shù)據(jù)表現(xiàn)不佳而提出來的新分布族,其擁有的可變尾部厚度、獨立變化的左右尾厚度及顯示的分位數(shù)函數(shù)的特征,使其在擬合金融數(shù)據(jù)時明顯優(yōu)于諸如正態(tài)分布,stable分布等經(jīng)典分布.自其提出以來,已成功應(yīng)用于國內(nèi)外證券市場、外匯市場、美國電力市場價格市場,以及流體力學(xué)中的湍流等的實證研究.然而,其參數(shù)估計,假設(shè)檢驗等重要的工作尚未有系統(tǒng)的研究工作出現(xiàn).本文主要研究了 Quantile第Ⅰ類分布的極大似然估計(MLE)的大樣本性質(zhì),成功證明了其參數(shù)的MLE的相合性和漸進(jìn)正態(tài)性.并通過應(yīng)用中心極限定理給出了此三個參數(shù)的假設(shè)檢驗及置信區(qū)間估計的理論結(jié)果.最后,用matlab軟件進(jìn)行了數(shù)值模擬.當(dāng)參數(shù)μ已知時,Quan-tile第Ⅰ類分布的其它三個參數(shù)的MLEs結(jié)果非常好;當(dāng)位置參數(shù)μ未知時,Quantile第Ⅰ類分布的四個參數(shù)的MLEs結(jié)果在樣本量很大的情況下也非常好.
[Abstract]:Quantile Class I distribution is a new distribution family proposed to overcome the poor performance of classical distribution in fitting financial yield data. It has the characteristics of variable tail thickness, independent left and right tail thickness and displayed quantile function. It is better than classical distribution such as normal distribution and stable distribution in fitting financial data. Since it was proposed, it has been successfully applied to the empirical studies of domestic and foreign stock markets, foreign exchange markets, American electricity market price markets, and turbulence in fluid dynamics. However, some important work, such as parameter estimation and hypothesis test, have not been systematically studied. In this paper, we study the large sample properties of maximum likelihood estimation (MLE) of Quantile class I distribution, and prove the consistency and asymptotic normality of MLE of its parameters. The hypothesis test of these three parameters and the theoretical results of confidence interval estimation are given by applying the central limit theorem. Finally, numerical simulation is carried out with matlab software. When the parameter 渭 is known, the MLEs results of the other three parameters of Quantile class I distribution are very good, and the MLEs results of the four parameters of the Quantile class I distribution are also very good when the position parameter 渭 is unknown.
【學(xué)位授予單位】：海南師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O212.1

【參考文獻(xiàn)】

相關(guān)期刊論文 前1條

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本文編號：2056055