在資料分析中，常遇到資料因檢測限制產生設限觀察值以及因異常觀察值所導致的厚尾與尖峰型態而產生統計分析上的挑戰。目前在多變量常態分配假設下的模型過於侷限，因其對於分佈偏離常態的資料缺乏穩健性。本文提出多變量雙指數設限迴歸(MDECR) 模型，用以同時穩健地描述具厚尾、尖峰與設限特性的多變量資料。為處理異質性多變量資料中的分群問題，進一步將MDECR 模型擴展為有限混合多變量雙指數設限迴歸(FM-MDECR) 模型，允許多個反應變數同時具備設限的情況。為進行模型參數之最大概似(ML) 估計，本文發展基於蒙地卡羅方法之期望值條件最大化（MCECM）演算法，並於MDECR 與FM-MDECR 模型中結合Metropolis-Hastings（MH）演算法以計算潛在變數之條件動差，並且使用Meilijson的方法計算基於訊息矩陣之參數標準誤估計。模擬研究顯示，所提出之模型與演算法在模型選擇、參數估計及分類準確度等方面具備顯著優勢，並探討本演算法所得之參數最大概似估計具有限樣本性質。最後，透過加州洋流汞資料與美國薪資水準資料集之分析，驗證所提方法之有效性與實用性。

In data analysis, it is common to encounter challenges in statistical analysis arising from censored measurements due to detection limits and heavy-tailed and leptokurtiz behavior owing to atypical observations. The models under the multivariate normality assumption are too restrictive as they suffer from the lack of robustness against departure from the normal distribution. The thesis proposes the Multivariate Double Exponential Censored Regression (MDECR) model to robustly describe multivariate data characterized by fat tails, leptokurtosis and censoring simultaneously. To address the issue of clustering heterogeneous multivariate data, we further extend the MDECR model to the Finite Mixture Multivariate Double Exponential Censored Regression (FM-MDECR) model, in which more than one response variables can be censored. To perform maximum likelihood (ML) estimation of the model parameters, we develop a Monte Carlo-based Expectation Conditional Maximization (MCECM) algorithm in which the Metropolis-Hastings (MH) algorithm is utilized to compute the conditional moments of the latent data in both the MDECR and FM-MDECR models. In addition, Meilijson’s method based on the information matrix is employed to compute the standard errors of parameter estimates. Simulation studies demonstrate the advantages of the proposed models in terms ofmodel selection, parameter estimation, and classification accuracy and investigate finite-sample properties of ML estimates obtained by our algorithms. Finally, we illustrate the validity and practical utility of the proposed methodology through the analysis of the California Coastal Current Mercury and U.S. Labor Market Earnings datasets.

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