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arXiv · 1810.02088

A Gaussian sequence approach for proving minimaxity: A Review

Yuzo Maruyama·William E. Strawderman
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Abstract

This paper reviews minimax best equivariant estimation in these invariant estimation problems: a location parameter, a scale parameter and a (Wishart) covariance matrix. We briefly review development of the best equivariant estimator as a generalized Bayes estimator relative to right invariant Haar measure in each case. Then we prove minimaxity of the best equivariant procedure by giving a least favorable prior sequence based on non-truncated Gaussian distributions. The results in this paper are all known, but we bring a fresh and somewhat unified approach by using, in contrast to most proofs in the literature, a smooth sequence of non truncated priors. This approach leads to some simplifications in the minimaxity proofs.

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Yuzo Maruyama, William E. Strawderman. 2018-10-04. A Gaussian sequence approach for proving minimaxity: A Review. https://arxiv.org/abs/1810.02088

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