Simultaneous equivariant estimation of the parameters of matrix scale and matrix location-scale models |
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Authors: | T Leo Alexander B Chandrasekar |
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Institution: | (1) Department of Statistics, Loyola College, 600034 Chennai, India |
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Abstract: | Eaton and Olkin (1987) discussed the problem of best equivariant estimator of the matrix scale parameter with respect to different
scalar loss functions. Edwin Prabakaran and Chandrasekar (1994) developed simultaneous equivariant estimation approach and
illustrated the method with examples. The problems considered in this paper are simultaneous equivariant estimation of the
parameters of (i) a matrix scale model and (ii) a multivariate location-scale model. By considering matrix loss function (Klebanov,
Linnik and Ruhin, 1971) a characterization of matrix minimum risk equivariant (MMRE) estimator of the matrix parameter is
obtained in each case. Illustrative examples are provided in which MMRE estimators are obtained with respect to two matrix
loss functions. |
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Keywords: | Equivariant estimation location-scale model scale model simultaneous estimation MMRE estimator |
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