Abstract
Consider the problem of estimating the mean of a p (≥3)-variate multi-normal distribution with identity variance-covariance matrix and with unweighted sum of squared error loss. A class of minimax, noncomparable (i.e. no estimate in the class dominates any other estimate in the class) estimates is proposed; the class contains rules dominating the simple James-Stein estimates. The estimates are essentially smoothed versions of the scaled, truncated James-Stein estimates studied by Efron and Morris. Explicit and analytically tractable expressions for their risks are obtained and are used to give guidelines for selecting estimates within the class.
Original language | English |
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Pages (from-to) | 359-369 |
Number of pages | 11 |
Journal | Journal of Statistical Planning and Inference |
Volume | 7 |
Issue number | 4 |
DOIs | |
State | Published - Jun 1983 |
Keywords
- Multivariate normal mean
- Stein estimates.