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

Abstract

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.

KEYWORDS:

• Censored data
• ECM algorithm
• Expected information matrix
• Mild outliers
• Truncated multivariate contaminated normal distribution

Supplementary Materials

Title: Supplementary Material: Multivariate Contaminated Normal Censored Regression Model: Properties and Maximum Likelihood Inference This supporting information contains: (JCGS-22-219R1-supp.pdf file)

1. Proofs of Theorem 2.1, 2.2, and 3.1;

2. Related formulae for derivations of standard errors for $\mathit{\mu }$;

3. Additional results for applications;

4. Results for the simulation.

Code and Data Availability Statement: Computer programs to perform the proposed method, as well as “VDEQ” and “Plasma” datasets used in Section 5 are available in “Data and Code.zip”.

Acknowledgments

The author is grateful to thank the Chief Editor, Associate Editor, and two anonymous referees for their insightful comments and suggestions that greatly improved the quality of this article.

Disclosure Statement

The author declared no conflict of interest.

Additional information

Funding

The author gratefully acknowledges the support of the National Science and Technology Council of Taiwan under grant number MOST 110-2118-M-006-006-MY3.