Comparison of Some Approaches to Optimization of Functional Statistical Modeling Algorithms in the Metric of the Space С

摘要

Functional algorithms of statistical modeling are used to eonstruct an approximation of the solution to a problem as a function on a given domain. Some approaches to the construction of upper error bounds in the metric of the space С with allowance for the degree of dependence of the estimates have been developed for functional algorithms with various types of stochastic estimate at nodes. There also exists a universal approach applicable to any dependence of stochastic estimates. The upper error bound constructed for the functional algorithm is used for choosing optimal values of parameters, such as the number of grid nodes and sample size. Optimality of the chosen parameters directly depends on the accuracy of the upper error bound used. The primary goal of the present paper is a comparison of the universal approach with those taking into account the degree of dependence of the estimates.