| 摘要: | 分析具有相關性的資料的一個流行的模型是 Copula。Copula 模型（Sklar，1959）是個方便建構聯合分 配函數（joint distribution function）的方法。此方法可將任意之邊際分配函數( marginal distribution function)透過相關性結構結合成聯合分配且提供了統計推論所需的概似函數（likelihood function）。但 是應用時少有人在乎模型對不對？當模型的假設與資料的分配不吻合時，是否造成錯誤的推論！ 本研究計劃想探知是否有那些 Copula 模型有較佳的強軔性。如gamma; Poisson; normal; negative binomial 與binomial 分配，在分析單維度資料時皆具有強軔性。如果做為Copula 模型的 marginal 分配時對Copula 模型的強軔性的影響為何?是賦予Copula 模型的強軔性，還是這些具單 維度分配之強軔性被Copula 模型破壞掉? 同時 Copula 模型一直未能在混合型資料(如:相關的(個數，連續)型資料)，相關的(個數，名目 (nominal)型資料)，相關的(名目，連續)型資料)的理論與應用有明顯的進展，此自然與Copula 在混 合型資料上的理論的複雜與困難有關。 為突破 Copula 在混合型資料上的困難，我們亦將試著以Royall and Tsou (2003)的強軔概似函數來 強軔化，分別如Poisson Gamma，Poisson Multinomial與Multinomial Gamma二分配假設為獨立的 模型。再將這些被強軔化的強軔概似函數與Copula(Poisson,Gamma)，Copula(Multinomial,Gamma)， Copula(Poisson,Multinomial)以及強軔的多維負二項比較它們在(1) 不偏性 (unbiasedness) (2) 有效性 (efficiency) 的表現。 ;Copula is a convenient method that manufactures multivariate distributions with specified desired marginal distributions. One can hence utilize copula for likelihood inference. However, one rarely pays attention to the property of robustness of copula. That is, how sensitive is the validity of inference derived from copula models when, in fact, data distributions do not conform to the model assumption? Can copula be made robust when model fails? There are several univariate distributions, including gamma, Poisson, normal, negative binomial and binomials that can be robustified under model misspecification. The objectives of this research project includes 1. Which, if any, copula models are more robust? 2. Copula models with gamma, Poisson, normal, negative binomial and binomials as marginals, can be robustified as the marginals? Or 3. The nice property of being robustifiable for these univariate distributions is destroyed by copula? Meanwhile, the copula technique falls short on the analysis of data of mixing types, such as correlated (count, continuous), (nominal, continuous), (count, nominal) data. This is certainly due to the theoretical difficulty for copula to incorporate correlated mixing data. We would also like to develop robust likelihood methods and make contrasts between copula models and several robust likelihood approaches in terms of validity and precision. |
