Acitas Sukru, Yenilmez Ismail, Senoglu Birdal, Kantar Yeliz Mert
Department of Statistics, Eskisehir Technical University, Eskisehir, Turkey.
Department of Statistics, Ankara University, Ankara, Turkey.
J Appl Stat. 2020 Jun 30;48(12):2136-2151. doi: 10.1080/02664763.2020.1786673. eCollection 2021.
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 -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.
众所周知，在误差项非正态的情况下，删失回归（CR）模型参数的经典托比特估计量是低效的。在本文中，我们建议在琼斯和法迪的偏态误差分布下使用修正最大似然（MML）估计量，该分布涵盖了广泛的偏态和对称分布，用于CR模型。明确给出了作为托比特估计量替代方案的MML估计量，并且它们渐近等同于最大似然估计量。进行了一项模拟研究，以比较MML估计量与普通最小二乘法、托比特法、删失最小绝对偏差法和对称截尾最小二乘法等经典估计量的效率。模拟研究结果表明，就CR模型的均方根误差准则而言，MML估计量在其他估计量中表现良好。还提供了一个实际例子来说明MML方法的适用性。
