Multivariate Contaminated Normal Censored Regression Model: Properties and Maximum Likelihood Inference

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摘要

The Multivariate Contaminated Normal (MCN) distribution which contains two extra parameters with respect to parameters of the multivariate normal distribution, one for controlling the proportion of mild outliers and the other for specifying the degree of contamination, has been widely applied in robust statistics in the case of elliptically heavy-tailed empirical distributions. This article extends the MCN model to data with possibly censored values due to limits of quantification, referred to as the MCN with censoring (MCN-C) model, and further establishes the censored multivariate linear regression model where the random errors have the MCN distribution, named as the MCN censored regression (MCN-CR) model. Two computationally feasible Expectation Conditional Maximization (ECM) algorithms are developed for maximum likelihood estimation of MCN-C and MCN-CR models. An information-based method is used to approximate the standard errors of location parameters and regression coefficients. The capability and effectiveness of the MCN-C and MCN-CR models are illustrated via two real-data examples. A simulation study is conducted to investigate the superiority of the proposed models in terms of fit, accuracy of parameter estimation and censored data recovery as compared with classical approaches. Supplementary materials for this article are available online.

原文English
頁(從 - 到)1671-1684
頁數14
期刊Journal of Computational and Graphical Statistics
32
發行號4
DOIs
出版狀態Published - 2023

All Science Journal Classification (ASJC) codes

  • 統計與概率
  • 離散數學和組合
  • 統計、概率和不確定性

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