In this paper we compare recently developed preliminary test estimator called Preliminary Test Stochastic Restricted Liu Estimator (PTSRLE) with Ordinary Least Square Estimator (OLSE) and Mixed Estimator (ME) in the M...In this paper we compare recently developed preliminary test estimator called Preliminary Test Stochastic Restricted Liu Estimator (PTSRLE) with Ordinary Least Square Estimator (OLSE) and Mixed Estimator (ME) in the Mean Square Error Matrix (MSEM) sense for the two cases in which the stochastic restrictions are correct and not correct. Finally a numerical example and a Monte Carlo simulation study are done to illustrate the theoretical findings.展开更多
The aim of this paper is to propose some diagnostic methods in stochastic restricted linear regression models. A review of stochastic restricted linear regression models is given. For the model, this paper studies the...The aim of this paper is to propose some diagnostic methods in stochastic restricted linear regression models. A review of stochastic restricted linear regression models is given. For the model, this paper studies the method and application of the diagnostic mostly. Firstly, review the estimators of this model. Secondly, show that the case deletion model is equivalent to the mean shift outlier model for diagnostic purpose. Then, some diagnostic statistics are given. At last, example is given to illustrate our results.展开更多
In the presence of multicollinearity in logistic regression, the variance of the Maximum Likelihood Estimator (MLE) becomes inflated. Siray et al. (2015) [1] proposed a restricted Liu estimator in logistic regression ...In the presence of multicollinearity in logistic regression, the variance of the Maximum Likelihood Estimator (MLE) becomes inflated. Siray et al. (2015) [1] proposed a restricted Liu estimator in logistic regression model with exact linear restrictions. However, there are some situations, where the linear restrictions are stochastic. In this paper, we propose a Stochastic Restricted Maximum Likelihood Estimator (SRMLE) for the logistic regression model with stochastic linear restrictions to overcome this issue. Moreover, a Monte Carlo simulation is conducted for comparing the performances of the MLE, Restricted Maximum Likelihood Estimator (RMLE), Ridge Type Logistic Estimator(LRE), Liu Type Logistic Estimator(LLE), and SRMLE for the logistic regression model by using Scalar Mean Squared Error (SMSE).展开更多
Ridge type estimators are used to estimate regression parameters in a multiple linear regression model when multicolinearity exists among predictor variables. When different estimators are available, preliminary test ...Ridge type estimators are used to estimate regression parameters in a multiple linear regression model when multicolinearity exists among predictor variables. When different estimators are available, preliminary test estimation procedure is adopted to select a suitable estimator. In this paper, two ridge estimators, the Stochastic Restricted Liu Estimator and Liu Estimator are combined to define a new preliminary test estimator, namely the Preliminary Test Stochastic Restricted Liu Estimator (PTSRLE). The stochastic properties of the proposed estimator are derived, and the performance of PTSRLE is compared with SRLE in the sense of mean square error matrix (MSEM) and scalar mean square error (SMSE) for the two cases in which the stochastic restrictions are correct and not correct. Moreover the SMSE of PTSRLE based on Wald (WA), Likelihood Ratio (LR) and Lagrangian Multiplier (LM) tests are derived, and the performance of PTSRLE is compared using WA, LR and LM tests as a function of the shrinkage parameter d with respect to the SMSE. Finally a numerical example is given to illustrate some of the theoretical findings.展开更多
In order to overcome the well-known multicollinearity problem, we propose a new Stochastic Restricted Liu Estimator in logistic regression model. In the mean square error matrix sense, the new estimation is compared w...In order to overcome the well-known multicollinearity problem, we propose a new Stochastic Restricted Liu Estimator in logistic regression model. In the mean square error matrix sense, the new estimation is compared with the Maximum Likelihood Estimation, Liu Estimator Stochastic Restricted Maximum Likelihood Estimator etc. Finally, a numerical example and a Monte Carlo simulation are given to explain some of the theoretical results.展开更多
文摘In this paper we compare recently developed preliminary test estimator called Preliminary Test Stochastic Restricted Liu Estimator (PTSRLE) with Ordinary Least Square Estimator (OLSE) and Mixed Estimator (ME) in the Mean Square Error Matrix (MSEM) sense for the two cases in which the stochastic restrictions are correct and not correct. Finally a numerical example and a Monte Carlo simulation study are done to illustrate the theoretical findings.
文摘The aim of this paper is to propose some diagnostic methods in stochastic restricted linear regression models. A review of stochastic restricted linear regression models is given. For the model, this paper studies the method and application of the diagnostic mostly. Firstly, review the estimators of this model. Secondly, show that the case deletion model is equivalent to the mean shift outlier model for diagnostic purpose. Then, some diagnostic statistics are given. At last, example is given to illustrate our results.
文摘In the presence of multicollinearity in logistic regression, the variance of the Maximum Likelihood Estimator (MLE) becomes inflated. Siray et al. (2015) [1] proposed a restricted Liu estimator in logistic regression model with exact linear restrictions. However, there are some situations, where the linear restrictions are stochastic. In this paper, we propose a Stochastic Restricted Maximum Likelihood Estimator (SRMLE) for the logistic regression model with stochastic linear restrictions to overcome this issue. Moreover, a Monte Carlo simulation is conducted for comparing the performances of the MLE, Restricted Maximum Likelihood Estimator (RMLE), Ridge Type Logistic Estimator(LRE), Liu Type Logistic Estimator(LLE), and SRMLE for the logistic regression model by using Scalar Mean Squared Error (SMSE).
文摘Ridge type estimators are used to estimate regression parameters in a multiple linear regression model when multicolinearity exists among predictor variables. When different estimators are available, preliminary test estimation procedure is adopted to select a suitable estimator. In this paper, two ridge estimators, the Stochastic Restricted Liu Estimator and Liu Estimator are combined to define a new preliminary test estimator, namely the Preliminary Test Stochastic Restricted Liu Estimator (PTSRLE). The stochastic properties of the proposed estimator are derived, and the performance of PTSRLE is compared with SRLE in the sense of mean square error matrix (MSEM) and scalar mean square error (SMSE) for the two cases in which the stochastic restrictions are correct and not correct. Moreover the SMSE of PTSRLE based on Wald (WA), Likelihood Ratio (LR) and Lagrangian Multiplier (LM) tests are derived, and the performance of PTSRLE is compared using WA, LR and LM tests as a function of the shrinkage parameter d with respect to the SMSE. Finally a numerical example is given to illustrate some of the theoretical findings.
文摘In order to overcome the well-known multicollinearity problem, we propose a new Stochastic Restricted Liu Estimator in logistic regression model. In the mean square error matrix sense, the new estimation is compared with the Maximum Likelihood Estimation, Liu Estimator Stochastic Restricted Maximum Likelihood Estimator etc. Finally, a numerical example and a Monte Carlo simulation are given to explain some of the theoretical results.
