Defining a two-parameter estimator: a mathematical programming evidence

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 …”

“…Aslam and Ahmad 56 proposed a new two‐parameter estimator by modifying the LE using the existing modified ridge‐type estimator. Most recently, Üstündağ Şiray et al 57 developed a new two‐parameter estimator which has many benefits from different aspects in the linear regression model since it combines the advantages of the RE and LE. Also, they investigated the selection of the shrinkage parameters utilizing both conventional and contemporary methods.…”

“…To take the advantages of two‐parameter estimation in the Tobit regression model, we propose a Tobit two‐parameter estimator based on the philosophy behind the two‐parameter estimator of Üstündağ Şiray et al 57 There are lots of two‐parameter estimators in the linear regression model. To prevent confusion regarding the name and to distinguish the two‐parameter estimator of Üstündağ Şiray et al 57 from the others, we call this estimator UTO ( Ü stündağ & T oker & Ö zbay) estimator from now on. Thus, we name our new Tobit two‐parameter estimator Tobit UTO (T‐UTO) estimator.…”

“…To take the advantages of two-parameter estimation in the Tobit regression model, we propose a Tobit two-parameter estimator based on the philosophy behind the two-parameter estimator of Üstünda g Şiray et al 57 There are lots of two-parameter estimators in the linear regression model. To prevent confusion regarding the name and to distinguish the two-parameter estimator of Üstünda g Şiray et al 57 We use simulated data to check the theoretical results and reach more comprehensive outcomes. For this purpose, Monte Carlo experiments are designed to examine censored data with various levels of factors.…”

Modified Kibria-Lukman (MKL) estimator for the Poisson Regression Model: application and simulation

“… The use of “hat” is missing while presenting some estimators. In the Introduction section, the manuscript Defining a two-parameter estimator: a mathematical programming evidence by Üstündağ Şiray et al (2021) 1 may be mentioned since this is a more recent article in which a new biased estimator is proposed to mitigate multicollinearity. On page 4, the authors should explain what lambdas are.…”