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    政大機構典藏 > 商學院 > 統計學系 > 學位論文 >  Item 140.119/89644
    Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/89644


    Title: 論混合常態分配之估計
    Authors: 李瑞蘭
    Contributors: 李隆安
    李瑞蘭
    Date: 1991
    1990
    Issue Date: 2016-05-02 17:02:53 (UTC+8)
    Abstract: 混合模式(mixture m。del) 參數的估計問題,研究迄今已近一世紀,自Pearson (1894) 提出動差法來估計兩個混合常態模式的參數,往後有許多學者繼續這個範疇的研究,且提出他們不同的估計法。而近半世紀以來,混合常態分配被廣泛應用在許多學科的進一步研究分析上,因此,它的參數估計的意義就更顯重要。
    我們欲估計兩個混合常態分配的參數,但原參數空間有識別性的問題,估計參數時會產生Chiang 等人所提的不好的現象,經過適當轉換後的新參數空間,則無識別性的問題。本文第一章簡單地介紹吾師李隆安博士所提的四個空間轉換函數和轉換後所對應的新參數空間。在第二章中,先簡單地介紹一些估計兩個混合常態參數的方法,然後再介紹現今最常用來估計兩個混合常態參數的方法- MLE ,其中包括估計MLE 的EM 演算法、牛頓法和最佳化循序演算法,並將Burnham (1988) 提出求解有限混合分配的最大概似估計值的縮減公式,應用在EM 演算法上,可知道五維參數EM 反覆求解法即三維參數EM 反覆求解法,可以縮減計算問題的大小。同時也介紹拋磚引玉法,其為一精深再抽樣的方法,它有系統的改進原始估計值及估計改進後估計式的變異數。在第三章中,對摸擬所需之資料組、反覆求解的式子和數值問題的解決方法做介紹。第四章中,針對EM法配合求解MLE 的縮減公式和最佳化循序演算法估計所得之兩個混合常態分配參數估計值做分析,並做原參數空間和新參數空間上EM 法收斂快慢的比較;此外並將應用拋磚引玉法,取一些特殊形式的統計量來估計參數的結果做記錄。 第五章,為結論與進一步研究。
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    黃瓊玉(1990),論混合常態之可識別性,政大統計所碩士論文
    Description: 碩士
    國立政治大學
    統計學系
    Source URI: http://thesis.lib.nccu.edu.tw/record/#B2002005031
    Data Type: thesis
    Appears in Collections:[統計學系] 學位論文

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