Modified maximum likelihood estimator for censored linear regression model with two-piece generalized t distribution

Chengdi Lian (), Camila Borelli Zeller (), Ke Yang () and Weihu Cheng ()
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Chengdi Lian: Beijing University of Technology
Camila Borelli Zeller: s/n - São Pedro - Juiz de Fora
Ke Yang: Beijing University of Technology
Weihu Cheng: Beijing University of Technology

Statistical Papers, 2025, vol. 66, issue 2, No 20, 45 pages

Abstract: Abstract In many fields, limited or censored data are often collected due to limitations of measurement equipment or experimental design. Commonly used censored linear regression models rely on the assumption of normality for the error terms. However, this approach has faced criticism in literature due to its sensitivity to deviations from the normality assumption. In this paper, we propose an extension of the CR model under the two-piece generalized t (TPGT)-error distribution, called TPGT-CR model. The TPGT-CR model offers greater flexibility in modeling data by accommodating skewness and heavy tails. We developed a modified maximum likelihood (MML) estimator for the proposed model and introduced the modified deviance residual to detect outliers. The developed MML estimator under the TPGT assumption possesses several appealing merits, including robustness against outliers, asymptotic equivalence to the maximum likelihood estimator, and explicit functions of sample observations. Simulation studies are conducted to examine the finite sample performance, robustness, and effectiveness of both the classical and proposed estimators. The results from both the simulated and real data illustrate the usefulness of the proposed method.

Keywords: Censored regression model; Two-piece generalized t distribution; Modified maximum likelihood; Residual analysis; Tobit model (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00362-024-01634-1

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