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Pre-test shrinkage estimator of the mean of a normal population. (English) Zbl 1010.62020

From the introduction: Consider a normal population \(N(\mu, \sigma^2)\), where \(\sigma^2\) is assumed to be known. Suppose \(\mu_0\) and \(\mu_1\) are two estimates of \(\mu\) obtained on two prior occasions. The problem is to find a shrinkage estimator of \(\mu\) based on the prior estimates \(\mu_0\) and \(\mu_1\). A preliminary test of the hypothesis \(H_0:\mu= \mu_0\) against \(H_1:\mu =\mu_1\) is first performed. On the outcome of this test, a shrinkage estimator of \(\mu\) is defined.

MSC:

62F10 Point estimation
62F03 Parametric hypothesis testing
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