Nonparametric Function Fitting in the Presence of Nonstationary Noise

The article refers to the problem of regression functions estimation in the presence of nonstationary noise. We investigate the model y(i) = R(x(i)) + epsilon(i), i = 1, 2, ... n, where xi is assumed to be the d-dimensional vector, set of deterministic inputs, x(i) is an element of S-d, y(i) is the scalar, set of probabilistic outputs, and epsilon(i) is a measurement noise with zero mean and variance depending on n. R(.) is a completely unknown function. One of the possible solutions of finding function R(.) is to apply non-parametric methodology - algorithms based on the Parzen kernel or algorithms derived from orthogonal series. The novel result of this article is the analysis of convergence for some class of nonstationarity. We present the conditions when the algorithm of estimation is convergent even when the variance of noise is divergent with number of observations tending to infinity. The results of numerical experiments are presented.