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研究生： 王价輝
Jie-Huei Wang
論文名稱： 分析二維個數資料之有母數強韌法
指導教授： 鄒宗山
Tsung-Shan Tsou
口試委員:
學位類別： 碩士
Master
系所名稱： 理學院 - 統計研究所
Graduate Institute of Statistics
畢業學年度： 94
語文別： 中文
論文頁數： 49
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    • 在處理二維個數資料時，為了分析時的便利，多數情況下都會假設資料服從二維卜瓦松分配或二維負二項分配。但是一旦資料不是來自二維卜瓦松分配或二維負二項分配時，那麼根據二維卜瓦松分配或二維負二項分配模型所做的統計推論便是錯誤的。
    本文將Royall and Tsou(2003)所提出的槪似函數修正法應用於二維個數資料之母體平均數之比率的推論上，說明所提出的二維卜瓦松實作模型和二維負二項實作模型是可以經過適當的修正而被強韌化。在大樣本時，且部分正規條件下，不論資料真正分配為何，據此強韌槪似函數可對母體平均數之比率參數做正確統計推論。

    This thesis utilizes the robust likelihood technique proposed by Royall and Tsou (2003) to develop parametric robust inferences about the comparison of two dependent populations of counts.
    More specifically, bivariate Poisson and bivariate negative binomial models are corrected to become robust. With large samples the two adjusted likelihood functions are asymptotically legitimate for the parameter of interest, without the knowledge of the true underlying distributions. Simulations are used to demonstrate the efficacy of the proposed robust method.

    目錄 第一章 緒論.........................................................................................1 第二章 強韌迴歸.................................................................................2 第三章 二維卜瓦松模型的修正項.....................................................4 3.1求參數的最大概似估計量.................................................................4 3.2 的計算..............................................................................................8 3.3 的計算............................................................................................17 第四章 二維負二項模型的修正項...................................................28 4.1求參數的最大概似估計量...............................................................28 4.2 的計算............................................................................................31 4.3 的計算............................................................................................34 第五章 模擬研究...............................................................................42 5.1資料生成...........................................................................................42 5.2模擬過程...........................................................................................43 5.3模擬結果...........................................................................................43 第六章 結論.......................................................................................47 第七章 參考文獻...............................................................................48

    1. Holgate, P(1964). Estimate for the bivariate Poisson distribution. Biometrika, 51, 1 and 2, 241-245.
    2. I.L. Solis-Trapala and V. T.Farewell(2005). Regression analysis of overdispersed correlated count data with subject specific covariates. Statistics in Medicine, 24, 2557-2575.
    2. Royall, R.M., and Tsou, T-S (2003). Interpreting statistical evidence using imperfect models: Robust adjusted likelihood functions. Journal of the Royal Statistical Society. Series B (Statistical Methodology), 65, 391-404.
    3. Tsou, T-S (2003). Comparing two population means and variances - a parametric robust way. Communications in Statistics - Theory and Methods, 32, 10, 2013-2019.
    4. Tsou, T-S and K-F Cheng (2004) Parametric robust regression analysis of contaminated data. Communications in Statistics - Theory and Methods, 33, 1887-1898.
    5. Tsou, T-S and Chien, L-C (2005). Parametric robust tests for multiple regression parameters under generalized linear models. Advances and Applications in Statistics, 1, 51-86.
    6. Tsou, T-S (2005a). Robust inferences for the correlation coefficient – a parametric robust way. Communications in Statistics - Theory and Methods, 34, 147-162.
    7. Tsou, T-S (2005b). Inferences of variance functions- a parametric robust way. Journal of Applied Statistics, Vol. 32:785-796.
    8. Tsou, T-S (2006a). Robust Possion regression. Journal of Statistical Planning and Inference, 136, 3173-3186.
    9. Tsou, T-S (2006b). A simple and exploratory way to determine the mean-variance relationship in generalized linear models. (to appear in Statistics in Medicine)

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