Least squares method with the use of ordering

Abstract

The estimation of unknown finite-dimensional parameter of nonlinear non-stationary regression is considered. The estimation method uses the ordering of squares of deviations sum on finite net of knots. The net approximates known restricted set of parameter values. The method of estimation analysis is proposed for the case of partial a priori uncertainty. A priori description supposes the knowledge of some standard regression function and numerical sequence corresponding to spectra of measurement errors. The method enables to obtain upper bounds for estimation error quantile and for the risks relative to general loss function. The example is considered.