Abstract:
This paper is devoted to the mean-square optimal stochastic recovery of a square integrable function with respect to the Lebesgue measure defined on a finite-dimensional compact
set. We justify an optimal recovery procedure for such a function observed at each point of its
compact domain with Gaussian errors. The existence of the optimal stochastic recovery procedure as well as its unbiasedness and consistency are established. In addition, we propose and
justify a near-optimal stochastic recovery procedure in order to: i) estimate the dependence of
the standard deviation on the number of orthogonal functions and the number of observations
and ii) find the number of orthogonal functions that minimizes the standard deviation.