What question did this study set out to answer?

To determine whether preliminary-test estimators are optimal for estimating the mean vector of a multivariate normal distribution under quadratic loss.

October 1, 1972The Annals of Mathematical StatisticsOpen Access

Non-Optimality of Preliminary-Test Estimators for the Mean of a Multivariate Normal Distribution

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To determine whether preliminary-test estimators are optimal for estimating the mean vector of a multivariate normal distribution under quadratic loss.
Evaluated the risk function of preliminary-test estimators under quadratic loss for general linear hypotheses concerning the mean vector.
Analyzed estimation risk under conditions where the covariance matrix is known up to a scalar multiple and where it is completely unknown.
While preliminary-test estimators yield lower risk than the standard estimator at specific parameter values, their risk exceeds that of the standard estimator across other regions of the parameter space.
Preliminary-test estimators are strictly dominated by the positive-part James-Stein estimator across all evaluated linear hypotheses.

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Implication

Theoretical analysis demonstrates non-optimality of preliminary-test estimators for multivariate normal mean vectors, highlighting dominance by the positive-part Stein-James estimator.

Cite This Study

Sclove et al. (1972) studied this question.

synapsesocial.com/papers/6a0f0c21a14f152feafa309e https://doi.org/10.1214/aoms/1177692380

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Implication

Theoretical analysis demonstrates non-optimality of preliminary-test estimators for multivariate normal mean vectors, highlighting dominance by the positive-part Stein-James estimator.

Non-Optimality of Preliminary-Test Estimators for the Mean of a Multivariate Normal Distribution

Key Points

Discussion

Implication

Cite This Study

Non-Optimality of Preliminary-Test Estimators for the Mean of a Multivariate Normal Distribution

Key Points

Discussion

Implication

Cite This Study

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