TY - JOUR
T1 - A Gaussian sequence approach for proving minimaxity
T2 - A Review
AU - Maruyama, Yuzo
AU - Strawderman, William E.
N1 - Funding Information:
This work was partially supported by JSPS KAKENHI16K00040, 18H00835, 19K11852.This work was partially supported by grants from the Simons Foundation (#418098 to William Strawderman).
Publisher Copyright:
© 2020 Elsevier B.V.
PY - 2021/3
Y1 - 2021/3
N2 - This paper reviews minimax best equivariant estimation in three 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.
AB - This paper reviews minimax best equivariant estimation in three 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.
KW - Equivariance
KW - Invariance
KW - Least favorable prior
KW - Minimaxity
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U2 - 10.1016/j.jspi.2020.06.007
DO - 10.1016/j.jspi.2020.06.007
M3 - Review article
AN - SCOPUS:85087770543
SN - 0378-3758
VL - 211
SP - 256
EP - 270
JO - Journal of Statistical Planning and Inference
JF - Journal of Statistical Planning and Inference
ER -