縱貫性相關資料之有母數強韌迴歸; Parametric Robust Regression for Longitudinal Correlated Data

Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/45879

Title:	縱貫性相關資料之有母數強韌迴歸;Parametric Robust Regression for Longitudinal Correlated Data
Authors:	鄒宗山
Contributors:	統計研究所
Keywords:	縱貫性資料;強韌概似函數;強韌珈瑪迴歸;強韌常態迴歸;變異數迴歸;Robust likelihoods;Robust gamma regression;Robust normal regression;Variance regression;數學類
Date:	2008-07-01
Issue Date:	2010-12-28 15:38:43 (UTC+8)
Publisher:	行政院國家科學委員會
Abstract:	Royall與Tsou (2003) 提出的強韌概似函數（robust likelihood function）的方法已被成功的推廣到廣義線性模型（generalized linear models, GLMs）的架構下迴歸的強韌推論上，見Tsou and Cheng (2004), Tsou (2005a), Tsou and Chien (2005) 及Tsou (2006a)。簡而言之，在GLMs架構下，如 ( ) ( ) i i E Y = g , i 0 i0 1 i1 p 2 ip 2 ip 1 x x x x . . . = + + + + , 0 1, i x = i =1,2, ,n 其中0 1 ( , , )T i i ip x x . x = 為i Y 的自變量向量，g(i)為一連結函數（link function），且1, , n Y Y 獨立，Tsou提出了對常態迴歸（normal regression）及珈瑪迴歸（gamma regression）的修正法。在大樣本的情形下，只要1, , n Y Y 的真正分配二階動有限，二種修正後的迴歸模型，都可對 0 2 ( , , , )T p . = 產生正確的統計推論。這種強韌迴歸的方法也被Tsou推廣到變異數函數的統計推論問題上。如，假設 ( ) ( ) i i Var Y = h , i 0 i0 1 i1 p 1 ip 1 x x x . . = + + + , 0 1, i x = i =1,2, ,n 其中h(i)為變異數之連結函數。Tsou證明，常態模型，經由適當修正後，可提供參數 ( ) 0 1 1 , , , T p . = 的強韌推論。相關文獻包括Tsou (2003), Tsou (2005b) 及 Tsou (2006b)。本計劃主要的工作是研究當反應變數具有相關性時，迴歸參數之有母數強韌推論的問題。目標是建立，不論有相關性資料的聯合機率分配為何都正確的推論方法。探討常態模型或珈瑪模型是否能被修正?如果能，又該如何的來修正，修正項為何？因此第一個目標便是建立修正法與修正項的推導工作。此階段的工作偏重於理論的建立與証明。當上述研究目標達成後，接下來便要將所建立起來的有母數的強韌推論法與GEE （generalized estimating equations）方式產生的結果比較相對的有效性（efficiency）。這部分的研究工作將會有較繁重的程式寫作與計算。本研究計劃完成後，將對縱貫性資料之迴歸分析，建立一個具有一般而言無母數方法才有的強韌性與有母數方法才有的有效性的有母數強韌推論法。此實為統計學上一個重大的突破！ The idea of robust likelihood function proposed by Royall and Tsou (2003) has been successfully extended to the generalized linear models setting for the mean regression problems. It has been made available the parametric robust inference about regression coefficients in the following model 0 0 1 1 0 [ ( )] , 1, g E Yi = xi + xi + + xip p xi = i = 1, , n where g is a link function, 0 ( , , ) p = is the vector of mean regression coefficients and 0 ( , , ) i i ip = x x x is the vector of characteristics specific to i y . With large samples, the legitimate likelihood function for any is provided whatever the true distributions are, so long the true underlying distributions have finite second moments. Related references include Tsou and Cheng (2004), Tsou (2005a), Tsou and Chien (2005) and Tsou (2006a). The robust regression methodology was also further extended to the inference of variance function ( ) i Var Y , where 0 1 1 [ ( )] i i p ip h Var Y = + x + + x Here h is the link function for the variance and 0 ( , , ) p = is the vector of regression coefficients of the variance function. Asymptotically valid likelihood function for was provided for general true distributions of theY 's , so long they have finite forth moments. References include Tsou (2003), Tsou (2005b), Tsou (2006b) and Tsou (2006c). In this project correlated response variables are considered. Parametric robust likelihood functions for regression coefficients will be developed. Focuses are on robust models for correlated continuous data and for correlated count data. The performance of the novel robust procedure will be compared to the popular GEE (generalized estimating equations) methodology. More specifically, robust varianceestimates of the GEE-estimates of based on GEE will be compared with obtained from the proposed parametric robust method. It is expected that the new parametric robust method is superior to the GEE approach, since GEE is semi-parametric. 研究期間：9608 ~ 9707
Relation:	財團法人國家實驗研究院科技政策研究與資訊中心
Appears in Collections:	[Graduate Institute of Statistics] Research Project

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