INADMISSIBILITY OF THE USUAL ESTIMATOR FOR THE MEAN OF A MULTIVARIATE NORMAL DISTRIBUTION¶
Stein. (1956). INADMISSIBILITY OF THE USUAL ESTIMATOR FOR THE MEAN OF A MULTIVARIATE NORMAL DISTRIBUTION. Contribution to the Theory of Statistics.
Cited by¶
1 citation across 1 artifact.
Domain-specific¶
- Stein's Paradox
- Stein's paradox (Charles Stein, 1956; James and Stein, 1961) is the result that the maximum-likelihood estimator for a vector of three or more unknown means — estimate each mean separately by its own sample mean — is inadmissible under total squared-error loss: there exists an estimator that achieves strictly lower expected total squared error for every possible value of the true parameter vector, regardless of what those values are and regardless of whether the parameters have any relationship to one another
Supported in partVerified against the publisher's abstract
“If the loss is the sum of squares of the errors, this estimator is admissible for n or equal to 2, but inadmissible for n more than or equal to 3.”
- Stein's paradox (Charles Stein, 1956; James and Stein, 1961) is the result that the maximum-likelihood estimator for a vector of three or more unknown means — estimate each mean separately by its own sample mean — is inadmissible under total squared-error loss: there exists an estimator that achieves strictly lower expected total squared error for every possible value of the true parameter vector, regardless of what those values are and regardless of whether the parameters have any relationship to one another
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