Modified maximum likelihood estimator under the Jones and Faddy's skew t-error distribution for censored regression model

Abstract

It is well-known that classical Tobit estimator of the parameters of the censored regression (CR) model is inefficient in case of non-normal error terms. In this paper, we propose to use the modified maximum likelihood (MML) estimator under the Jones and Faddy's skew t-error distribution, which covers a wide range of skew and symmetric distributions, for the CR model. The MML estimators, providing an alternative to the Tobit estimator, are explicitly expressed and they are asymptotically equivalent to the maximum likelihood estimator. A simulation study is conducted to compare the efficiencies of the MML estimators with the classical estimators such as the ordinary least squares, Tobit, censored least absolute deviations and symmetrically trimmed least squares estimators. The results of the simulation study show that the MML estimators work well among the others with respect to the root mean square error criterion for the CR model. A real life example is also provided to show the suitability of the MML methodology.

Keywords:

• Censored regression model
• Tobit
• Jones and Faddy's skew t distribution
• modified maximum likelihood
• efficiency

2010 Mathematics Subject Classifications:

• 62J05
• 62F35
• 62F10

Acknowledgments

This study was supported by Eskisehir Technical University Scientific Research Projects Commission under the grant no: 1610F661 and the grant no: 19ADP093. We would like to thank to the Editors and anonymous referees for their constructive comments on an earlier version of this manuscript which resulted in this improved version. We would also like to thank to TURKSTAT for providing the Household Labour Force Survey (HLFS) data.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This study was supported by Eskisehir Technical University Scientific Research Projects Commission under the grant no: 1610F661 and the grant no: 19ADP093.