Improvement of Some Multidimensional Estimates by Reduction of Dimensionality

We consider in this paper a set of kp-variates from which k unbiased estimates of a multidimensional parameter are obtained. Our goal is to propose an improvement of those estimates based on projections onto lower dimensional spaces. The quality of estimation is measured by the mean square error (MSE) of estimation. Asymptotic expansion of these MSEs are given and estimates of these MSEs are proposed for practical use. Finally, several examples of applications are given.