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標題: 具自迴歸相依性與條件異質性之成長曲線分析
Analysis of the growth curve model with autoregressive dependence and conditional heteroscedasticity
作者: 廖宮毅
Liao, Gong Yi
關鍵字: growth curve;成長曲線;autoregressive dependence;heteroscedasiticity;Markov Chain Monte Carlo;自迴歸相依性;異質性;馬可夫鏈-蒙地卡羅
出版社: 應用數學系所
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本文之趣旨為討論具一次自迴歸相依性及一次條件異質性之成長曲線分析.在此假設下所得之多變量常態分佈的概似度函數及其數學性質詳述文中. 作者亦考量了從最大概似估計法觀點及貝氏估計觀點所引導之不同的參數估計法及預測法,在考量最大概似度估計參數時,作者給出了一數值演算方法以求得參數數值解,在考量貝氏估計時,作者使用了馬可夫鏈-蒙地卡羅法以求參數的事後分佈. 作者文中提供了具趣旨所揭之假設條件下的條件估計式及擴充估計式並以實務資料與模擬資料以說明此一成長曲線模式於參數估計與預測觀測值上之表現與效益

The growth curve model that the covariance matrix constructed with autoregressive (AR) dependence of degree 1 and autoregressive conditional heteroscedasiticity (ARCH) of degree 1 is studied in the thesis. The specification of the multivariate normal distribution with these two properties is dedicated. I consider both maximum likelihood inference perspective and Bayesian inference perspective for estimation and prediction. An algorithm is introduced for determining maximum likelihood estimates of the unknown parameters, on the other hand, Markov Chain Monte Carlo methods are elaborated for Bayesian estimation and prediction. The forms of the condictional predictor and extended predictor are provided and illustrated with numerical results of both real data and simulated data
其他識別: U0005-2306200614190000
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