Tobit Liu estimation of censored regression model: an application to Mroz data and a Monte Carlo simulation study

Two‐parameter estimation forTobitmodel: An application to national health and nutrition examination survey dataset

“…Toker et al 36 developed the following censored log‐likelihood function by adding a penalization term to Equation () $$$$ {Q}_{TLE}=\log L\left(X;\beta, {\sigma}^2\right)+\frac{1}{2{\sigma}^2}{\left(\beta -d\hat{\beta}\right)}^{\prime}\left(\beta -d\hat{\beta}\right), $$$$ where $$$ \frac{1}{2{\sigma}^2} $$$ is a Lagrangian multiplier, $$$ d $$$ is the Liu biasing parameter in the interval $$$ \left(0,1\right) $$$ and $$$ \hat{\beta} $$$ is the T‐MLE attained in the final iteration. Although Toker et al 36 took the interval of $$$ d $$$ as $$$ 0<d<1 $$$, this interval can be extended to $$$ -\infty <d<\infty $$$ (see 26,57 ). With the help of Equation (), they obtained the final form of the T‐LE as …”

“…Provided that the initial step value of the T‐MLE is equal to the initial step value of the T‐LE, finally Toker et al 36 defined the initial step T‐LE as follows: $$$$ {\hat{\beta}}_{TLE}^{(1)}={\left({X}^{\prime }{\hat{\Omega}}^{(0)}X+I\right)}^{-1}\left({X}^{\prime }{\hat{\Omega}}^{(0)}X+ dI\right){\hat{\beta}}^{(1)}, $$$$ where $$$ {\hat{\Omega}}^{(0)} $$$ is calculated at $$$ {\beta}^{(0)} $$$. In the case that $$$ d=1 $$$, the initial step T‐LE reduces to the initial step T‐MLE.…”

“…After the T‐RE was defined by Khalaf et al, 23 Toker et al 36 proposed the T‐LE and examined the theoretical properties of both the T‐RE and T‐LE in detail. They put forward that these estimators serve the purpose of eliminating the multicollinearity in the Tobit regression model.…”

“…As for the Liu estimator (LE), there are also lots of articles in linear regression model and some of them are listed as Liu, 25 Kaçıranlar et al, 26 Sakallıoğlu et al, 27 Liu, 28 Shukur et al, 29 Ebaid et al, 30 Lukman et al, 31 and Qasim et al 32 In logistic regression model, Urgan and Tez, 33 Mansson et al 34 and Üstündağ Şiray et al 35 are the studies which focus on the Liu estimation. Toker et al 36 introduced the Tobit Liu estimator (T‐LE) for the Tobit regression model and compared it with Tobit ridge estimator (T‐RE) and the T‐MLE. They also suggested some methods for selecting the unknown biasing parameter.…”

“…For this purpose, Monte Carlo experiments are designed to examine censored data with various levels of factors. When the literature is perused, Monte Carlo simulation studies for the censored regression models are encountered as in the papers of Leung and Yu, 71 Yu and Stander, 72 Caudill, 73 Khalaf et al, 23 Arık et al, 74 Zuehlke, 75 Kobayashi, 76 Yenilmez et al, 77 Alhusseini and Georgescu, 78 Yenilmez and Kantar, 79 Liu et al, 80 Lachos et al, 81 Yenilmez et al, 82 Acıtaş et al, 83 and Toker et al 36 Among the aforementioned articles just Khalaf et al 23 and Toker et al 36 investigated the multicollinearity problem in their Monte Carlo scenarios. In this article, we also examine the effect of multicollinearity in the simulation design dealing with various levels of factors like the number of independent variables, sample size, correlation degree, variance, and censorship.…”