Estimation of Slope for Linear Regression Model with Uncertain Prior Information and Student-t Error

Shahjahan Khan, A. K. Md. E. Saleh
2008 Communications in Statistics - Theory and Methods  
This paper considers estimation of the slope parameter of the linear regression model with Student-t errors in the presence of uncertain prior information on the value of the unknown slope. Incorporating uncertain non-sample prior information with the sample data the unrestricted, restricted, preliminary test, and shrinkage estimators are defined. The performances of the estimators are compared based on the criteria of unbiasedness and mean squared errors. Both analytical and graphical methods
more » ... graphical methods are explored. Although none of the estimators is uniformly superior to the others, if the non-sample information is close to its true value, the shrinkage estimator over performs the rest of the estimators. Keywords and Phrases: Multiple regression model; Student-t errors; preliminary test and shrinkage estimators; bias, mean square error and relative efficiency; mixture distribution of normal and inverted gamma; non-central chi-square and F distributions; and incomplete beta ratio.
doi:10.1080/03610920802040399 fatcat:wswnsptmdvg3jbn55g6np2zgim