Efficiency of shrinkage pretest estimator for the intercept parameter in simple linear regression model

Authors
mehran naghizadeh qomi
zohreh mahdizadeh
Abstract
Usually, the traditional estimation methods is used to estimate Parameters of the linear regression model, such as least-squared error method. Sometimes the researcher has information about the unknown intercept parameter as a guess that is called as non-sample prior information. In this article, a preliminary test estimator for the intercept parameter of the simple linear regression according to the non-sample prior information is introduced and the value of its risk function under the reflected normal loss function is investigated. Also, the behavior of shrinkage pretest estimator is compared with respect to the least-squares estimator using a simulation. The intervals where the shrinkage pretest estimator has the least risk compared to the least-squares estimator presented. The results show that the shrinkage pretest estimator outperforms the least-squares estimator when non-sample prior information is close to the real value. Also, the optimum value of the significant level of test is determined using max-min method. Then, proposed estimators are compared using a real data set.
Keywords
Prior information
shrinkage pretest estimator
Reflected normal loss function
Khan, S., Hoque, Z., A.K.M.E. Saleh. (2005). Estimation of the Intercept Parameter for Linear Regression Model with Uncertain Prior Information, Statistical Papers, 46(3), 379-398.



Hoque, Z., Hossain, S. (2012), Improved Estimation in Regression with Varying Penalty, Journal of Statistical Theory and Practice, 6, 260-273.



Hoque, Z., Khan, S., Wesolowski, J., (2009), Performance of Preliminary Test Estimator Under Linex Loss Fonction , Journal of Communications in StatisticsTheory and Methods, 38, 252-261.



Montgomery, D.C., Peck, E.A., Vining, G.G., (2012), Introduction to Linear Regression Analysis,5th Edition, Wiley.



Naghizadeh Qomi, M., and Kiapour, A.(2016), Improving the MLE of the Location Parameter of a Normal Population under Reflected Normal Loss, 47th Annual Iranian Mathematics Conference , Kharazmi University, karaj Iran.



Naghizadeh Qomi, M., Nematollahi, N., Parsian, A. (2012), Estimation After Selection Under Reflected Normal Loss Function, Communications in StatisticsTheory and Methods, 41, 1040-1051.



Spring, F. (1993), The Reflected Normal Loss Function, Canadian Journal of statistics, 21(1), 321-330.



Thompson, J.R. (1968), Some shrunken techniques for estimating the Mean, Journal of the American Statistician Association,, 63, 113-122.



Towhidi, M., Behoodian, J. (2001), Estimation of a Location Parameter with a Reflected Normal Loss function . Iranian Journal of Science and Technology, 25, 183-190.
Mathematical Research
Volume 9, Issue 2 - Serial Number 25
Summer 2023
Pages 125-145