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Reduction of Linear Models Using Correct or Incorrect Prior Information
Author(s) -
Toutenburg H.
Publication year - 1985
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710270305
Subject(s) - mathematics , estimator , reduction (mathematics) , linear model , statistics , prior information , prior probability , unbiased estimation , computer science , bayesian probability , artificial intelligence , geometry
When there is no prior knowledge on the parameter vector β of the linear model then the LSE is most favourable at least in the class of linear unbiased estimators. On the other hand, in many practical problems one has some guessed estimate of β. Using this information leads to two‐step estimation procedures which may or may not dominate the LSE with respect to MSE. The dominance depends on the degree of incorrectness of the guessed parameter and is analyzed numerically for the case of sample reduction.