On Minimum Variance Unbiased Estimation of a Power of an Unknown Scalar or Matrix

This thesis extends work on finding optimal estimates of Pt, both in the case where P is a scalar, and when P is a matrix. In the scalar case, we present a formula for minimum variance unbiased estimates of Pt, given k independent observations of the scalar P. We discuss the generalization to the matrix case, and compare the new estimate to the unbiased estimate presented by Kuznetsov and Orlov. We compare the estimates in terms of variance and computation. This comparison is done both theoretically and computationally