Comparison of approaches to optimization of functional statistical modeling algorithms in the metric of the space~$\mathbf C$

E. V. Shkarupa

Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 18 (2015) no. 2, pp. 219-234

Résumé

Functional algorithms of the statistical modeling are designed to construct an approximation of the problem solution as function on a required domain. The approaches to construction of the upper error bound in the metrics of the space $\mathbf C$ with allowance for the degree of dependence of the estimates were devised for functional algorithms with different types of stochastic estimates in the nodes. Furthermore, there exists a universal approach applicable at any degree of dependence. The constructed upper error bound of the functional algorithm is used for choosing an optimal value of parameters, such as the number of grid nodes and the sample size. Optimality of the chosen parameters directly depends on the accuracy of the used upper error bound. The primary intent of the present paper is a comparison of universal approaches and those with allowance for the degree of dependence of the estimates.