Finite mixture modeling of censored and missing data using the multivariate skew-normal distribution

作     者：de Alencar, Francisco H. C. Galarza, Christian E. Matos, Larissa A. Lachos, Victor H. 

作者机构：Univ Estadual Campinas Dept Estat Campinas SP Brazil ESPOL Escuela Super Politecn Litoral Fac Ciencias Nat & Matemat Guayaquil Ecuador Univ Connecticut Dept Stat Storrs CT 06269 USA 

出 版 物：《ADVANCES IN DATA ANALYSIS AND CLASSIFICATION》 (数据分析与分类进展)

年 卷 期：2022年第16卷第3期

页      面：521-557页

核心收录：

学科分类：081203[工学-计算机应用技术] 08[工学] 0714[理学-统计学（可授理学、经济学学位）] 0835[工学-软件工程] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：The authors are grateful to the Editor  Associate Editor and the referees for their helpful comments on an earlier version of this paper 

主　　题：Censored data Detection limit EM-type algorithms Finite mixture models Multivariate skew-normal distribution Truncated distributions 

摘      要：Finite mixture models have been widely used to model and analyze data from a heterogeneous populations. Moreover, data of this kind can be missing or subject to some upper and/or lower detection limits because of the constraints of experimental apparatuses. Another complication arises when measures of each population depart significantly from normality, such as asymmetric behavior. For such data structures, we propose a robust model for censored and/or missing data based on finite mixtures of multivariate skew-normal distributions. This approach allows us to model data with great flexibility, accommodating multimodality and skewness, simultaneously, depending on the structure of the mixture components. We develop an analytically simple, yet efficient, EM-type algorithm for conducting maximum likelihood estimation of the parameters. The algorithm has closed-form expressions at the E-step that rely on formulas for the mean and variance of the truncated multivariate skew-normal distributions. Furthermore, a general information-based method for approximating the asymptotic covariance matrix of the estimators is also presented. Results obtained from the analysis of both simulated and real datasets are reported to demonstrate the effectiveness of the proposed method. The proposed algorithm and method are implemented in the new R package CensMFM.