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Equivalence of the ( , ) m N I Problem and The Regression Problem With m Nuisance Parameters | ||
| Al-Mustansiriyah Journal of Science | ||
| Article 1, Volume 19, Issue 5, 2008, Pages 39-54 | ||
| Author | ||
| Sami D. Gabbara | ||
| Abstract | ||
| In this paper, we study the estimation of the unknown mean vector of parameters of a multivariate normal distribution when the disturbance variance 2 is known ( 1 2 ). The main estimation methods have been discussed along with their properties and the properties of the estimators. The focus is concentrated on the shrinkage method for finding the estimators. We wish to prove that there is a relationship between the shrinkage estimator b (the estimator of vector of parameters in the linear regression model in the presence of a vector of m nuisance parameters) and of ( , ) m N I , where for each estimator t(ˆ) (ˆ)ˆ for ( , ) m N I problem, there will be a corresponding weighted average least squares (WALS) estimator in the regression problem of the form u r b (ˆ)b (1(ˆ))b . | ||
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