Statistical Papers

, Volume 46, Issue 3, pp 379–395

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

  • Shahjahan Khan
  • Zahirul Hoque
  • A. K. Md. E Saleh

DOI: 10.1007/BF02762840

Cite this article as:
Khan, S., Hoque, Z. & Saleh, A.K.M.E. Statistical Papers (2005) 46: 379. doi:10.1007/BF02762840


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.

Key words

Regression modeluncertain non-sample prior informationmaximum likelihood, restricted, preliminary test and shrinkage estimatorsbias, mean square error and relative efficiency

AMS 1990 Subject Classification

Primary 62F30Secondary 62H12 and 62F10

Copyright information

© Springer-Verlag 2005

Authors and Affiliations

  • Shahjahan Khan
    • 1
  • Zahirul Hoque
    • 1
  • A. K. Md. E Saleh
    • 2
  1. 1.Department of Maths and ComputingUniversity of Soutern QueenslandToowoombaAustralia
  2. 2.School of Mathematics and StatisticsCarleton UniversityOttawaCanada
  3. 3.Dept of StatisticsUniversity of ChittagongBangladesh