Stable estimation of ratios of random functions from experimental data

Abstract

We describe a procedure for the synthesis of stable evaluations for a class of ratios, including many statistical characteristics appearing in the processing of experimental data, like the asymmetry coefficients and kurtosis of a distribution, the coefficient of variability of a sampling, dispersion relations, sample correlation coefficients, nonparametric regression estimates, and others. Asymptotic expansions of the proposed estimates are performed, and their mean square convergence is proved. As an example, we consider the stable nonparametric evaluation of a regression function.