Estimation of the intercept parameter for linear regression model with uncertain non-sample prior information

This paper considers alternative estimators of the intercept parameter of the linear regression model with normal error when uncertain non-sample prior information about the value of the slope parameter is available. The maximum likelihood, restricted, preliminary test and shrinkage estimators are considered. Based on their quadratic biases and mean square errors the relative performances of the estimators are investigated. Both analytical and graphical comparisons are explored. None of the estimators is found to be uniformly dominating the others. However, if the non-sample prior information regarding the value of the slope is not too far from its true value, the shrinkage estimator of the intercept parameter dominates the rest of the estimators.     

Improved estimation of the mean vector for student-t model

Improved James-Stein type estimation of the mean vector μ of a multovaroate Student-t population of dimension p with ν degrees of freedom is considered. In addition to the sample data, uncertain prior information on the value of the mean vector, in the form of a null hypothesis, is used for the estiamtion. The usual maximum liklihood estimator((mle) of μ is obtained and a test statistic for testing H₀:μ=μ₀ is derived. Based on the mle of μ and the tes statistic the preliminary test estimator (PTE), Stein-type shrinkage estimator (SE) and positive-rule shrinkage esiimator (PRSE) are defined. The bias and the quadratic risk of the estimators are evaiuated. The relative performances of the estimators are mvestigated by analyzing the risks under different condltlons It is observed that the FRSE dommates over he other three estimators, regardless of the vaiidity of the null hypothesis and the value ν.