Improved confidence set estimators of a multivariate normal mean and generalizations
โ Scribed by Fanny Ki; Kam-Wah Tsui
- Publisher
- Springer Japan
- Year
- 1985
- Tongue
- English
- Weight
- 612 KB
- Volume
- 37
- Category
- Article
- ISSN
- 0020-3157
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
We consider confidence sets for the mean of a multivariate normal distribution with unknown covariance matrix of the form \_ 2 I. The coverage probability of the usual confidence set is shown to be improved asymptotically by centering at a shrinkage estimator.
Let X1,..., XN be independent observations from Np(#, ~1) and Y1,..., YN be independent observations from Np(#, ~2). Assume that Xi's and Y~'s are independent. An unbiased estimator of/z which dominates the sample mean X for p \_> 1 under the loss function L(/z,/2) --(f~ -#)'~i-l(fL -/~) is suggeste
The problem of estimating the mean of a multivariate normal distribution is considered. A class of admissible minimax estimators is constructed. This class includes two well-known classes of estimators, Strawderman's and Alam's. Further, this class is much broader than theirs.