數據經常包含異常觀測值與因定量分析的檢測限制生成的設限觀察值。本文提出了多變量斜線設限迴歸(MSLCR) 模型穩健的對含有這類現象的資料進行建模。考慮到異質多變量數據的分群問題，特別是在存在異常值和設限的情況下，我們進一步延伸了有限混合多變量斜設限迴歸(FM-MSLCR) 模型，這是一種將有限混合模型與MSLCR 模型概念上簡單融合的模型。為了對模型參數進行最大概似估計，我們提供了基於蒙特卡羅基礎的期望條件最大化(MCECME) 演算法，其中Metropolis-Hastings(MH) 演算法被用來計算MSLCR 和FM-MSLCR 模型中的潛在變數的條件動差。並且使用一般化信息矩陣法來近似參數估計量的漸進標準誤。模擬結果顯示，所提出的模型和方法在MCECME 演算法的收斂行為、模型選擇、有限樣本的參數估計特性和分類性能方面具有優越性。最後，我們通過分析最後，我們通過分析「B-horizon 的地球化學元素含量」、「加州洋流系統中的溶解汞形態」來闡述所建構的模型方法之正確性與實用性。

Data may frequently contain atypical observations and censored measurements due to experimental detection limitations of the quantification assay. The thesis presents the multivariate-slash censored regression (MSLCR) model for robust modeling of data with such phenomena. Considering the problem of clustering heterogeneous multivariate data with outliers and censoring, we further propose the finite mixture of multivariate-slash censored regression (FM-MSLCR) model, which is conceptually a straightforward fusion of the finite mixture model and the MSLCR model. And, to perform maximum likelihood estimation of the model parameters, the Monte-Carlo based expectation conditional maximization either (MCECME) algorithms are provided, where the Metropolis-Hastings (MH) sampling procedures are used to calculate the conditional moments of latent data in the MSLCR and FM-MSLCR models. Then, a general information matrix-based method is used to approximate the asymptotic standard errors of the parameter estimators. The numerical results from simulations show the advantage of the proposed models and methods in the sense of convergence behavior of MCECM algorithms, model selection, finite sample properties of parameter estimates, and classification performance. Finally, we show the utilities of the proposed models by analyzing the data collected from the dissolved mercury speciation in the 「Geochemistry of B-horizon」and 「California current system」to illustrate the correctness and practicality of the constructed model method.

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