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Shrinkage Pre‐Test Estimator of the Intercept Parameter for a Regression Model with Multivariate Student‐t Errors
Author(s) -
Khan Shahjahan,
Md. Ehsanes Saleh A. K.
Publication year - 1997
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.4710390202
Subject(s) - mathematics , statistics , estimator , multivariate statistics , minimax , shrinkage , regression analysis , mean squared error , degrees of freedom (physics and chemistry) , multivariate normal distribution , shrinkage estimator , minimax estimator , minimum variance unbiased estimator , mathematical optimization , physics , quantum mechanics
In the presence of an uncertain prior information about the value of the slope parameter, the estimation of the intercept parameter of a simple regression model with a multivariate Student‐t error distribution is investigated. The unrestricted, restricted and shrinkage preliminary test maximum likelihood estimators are defined. The expressions for the bias and the mean square error of the three estimators are provided and the relative efficiences are analyzed. A maximin criterion is established, and graphs are constructed for an arbitrary number of degrees of freedom (D.F.) as well as sample sizes. A criterion to select optimal significance level is also discussed.