Procedure of a nonparametric estimation of terminal type functionals and its application in economic and engineering applications

The problem of an estimation of functionals of terminal type H((tau) over right arrow((x) over right arrow)) = H(F((0) over right arrow)((x) over right arrow F(r(1))((x) over right arrow),...,F(($) over right arrow (s))) on samples of stationary random quantities is considered. Here H : Rs+1 -> R-1 is a known function, and (x) over right arrow is an element of R-m - is fixed, on stationary sampling weekly dependent random quantities with an unknown distribution function F(i). The procedure implementing the two-step plan of a nonparametric estimation of the given functional is proposed. On the first step by means of truncation operation to an initial functional G(F((0) over right arrow)((x) over right arrow),F(($) over right arrow (1))((x) over right arrow),...,F((r) over right arrow (s))((x) over right arrow)) puts in correspondence a functional from a class of "sectional" functionals G(($) over right arrow (n)) is an element of P-C,P-gamma(H); on second - statistics substitution (t) over right arrow (n) equivalent to (F-n ((0) over right arrow)((x) over right arrow),F-n((r) over right arrow (1))((x) over right arrow),......,F-n((r) over right arrow (s)) (($) over right arrow)) into place (tau) over right arrow in a functional G(tau) is produced. Convergence in mean square of estimates is proved. Velocity of convergence CKO of proposed sectional nonparametric estimates at observance of some regularity conditions superimposed on H : Rs+1 -> R-1 and F((x) over right arrow), beyond all bounds approaches with lower bound of convergence CKO in parametric setting. The most important performance of the proposed procedure of an estimation is its scalability as it does not depend on a specific view of mapping and allocation of initial sampling. The given procedure can be used for the solution of various practical problems of economy and technics. As an example the recognition problem spatially distributed stochastic objects on the basis of functional scaling and a nonparametric estimation of a density function of sampling of descriptors of observable objects is considered.