Optimal Observation Directions for Estimating a Vector

摘要

To estimate a k-dimensional vector mu observations x(sub 1) to x(sub n) withrandom errors of the projections of mu in n given directions are used. The data can also be applied to test for bias of the observations. The problem discussed is how to choose directions to optimize these statistical procedures. The random variables x(sub 1) to x(sub n) are assumed to be uncorrelated with the same variance and normally distributed. Optimization criteria are: minimizing mean square error of the estimate and maximizing the power of the test.