Abstract
In estimation of the variance of a distribution with unknown mean, the paper suggests the linear shrinkage estimators motivated from a Bayesian perspective. The so-called Stein’s truncated estimator of the variance can be derived as the linear shrinkage estimator when the distribution is normal. The method of the linear shrinkage estimation is extended to non normal distributions and to linear regression models. The linear shrinkage estimator with the optimal weight estimate, derived without assuming normality, is shown to have a good numerical performance for several distributions.
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