Equivariant estimation of a mean vector [mu] of N([mu], [Sigma]) with [mu]'[Sigma]-1[mu] = 1 or [Sigma]-1/2[mu] = c or [Sigma] = [sigma]2[mu]'[mu]l

Takeaki Kariya, N. C. Giri and F. Perron

Journal of Multivariate Analysis, 1988, vol. 27, issue 1, 270-283

Abstract: This paper considers the problems of estimating a mean vector [mu] under constraint [mu]'[Sigma]-1[mu] = 1 or [Sigma]-1/2[mu] = c and derives the best equivariant estimators under the loss (a - [mu])' [Sigma]-1(a - [mu]), which dominate the MLE's uniformly. The results are regarded as multivariate extensions of those with known coefficient of variation in a univariate case. As a particular case for [mu]'[Sigma]-1[mu] = c, the case [Sigma] = [sigma]2[mu]'[mu]I is also treated.

Keywords: equivariant; estimation; best; equivariant; coefficient; of; variation; MLE; ancillary; statistics; maximal; invariant (search for similar items in EconPapers)
Date: 1988
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