Application of spectral analysis to minimax estimation (Q1322705)

We are concerned with minimax estimation of linear functionals when the parameter space is an ellipsoid in Hilbert space. In the case of countably infinite dimensional observations, a sufficient condition is given for \textit{P. Speckman}'s (unpublished manuscript) minimax linear estimator to be first order asymptotically minimax. The main idea in proving this result is to create an appropriate sequence of Bayes estimators in which the Bayes risk coincides asymptotically with the minimax linear risk. The analysis of the continuous time observations is also studied. In this case we present a method to transform the continuous time observations to the one with countably infinite independent observations. The method is using the singular value decomposition of a compact operator to define a stochastic linear functional on the observations.