The Unbiased Estimation Theory and the Multidimensional Bhattachryya Bounds.

Five decades ago, Bhattacharyya established a series of lower bounds for the variance of an unbiased estimator, since then called the Bhattacharyya bounds. In 1974 Blight and Rao have shown that the series of Bhattacharyya bounds converges to the variance of the best unbiased estimator. In this paper, we give an explicit formula of the minimum variance unbiase d estimator for a multidimensional parametric function and we obtain a multidimensional extension of Blight and Rao's result.