Mathematical Researches

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naghizadeh qomi M, mahdizadeh Z. Efficiency of shrinkage pretest estimator for the intercept parameter in simple linear regression model. mmr 2023; 9 (2) :125-145
URL: http://mmr.khu.ac.ir/article-1-3157-en.html

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.