A note on optimal vector unbiased predictor.

A characterization of optimal vector unbiased predictor is obtained. Some properties of optimal unbiased predictors are established. It is shown that simultaneous prediction of future random variables is equivalent to marginal prediction of these random variables. Following Kale and Chandrasekar (1983) and Chandrasekar (1984), it is shown that the criteria proposed by ishii (1969) based on matrices and the one proposed by Bibby and Toutenburg (1977) based on quadratic loss in the class of vector unbiased predictors are equivalent. The above approach is illustrated with some examples. [ABSTRACT FROM AUTHOR]