ESTIMATING NONLINEAR REGRESSION ERRORS WITHOUT DOING REGRESSION
Hong Pi and Carsten Peterson
Abstract: A method for estimating nonlinear regression errors and their
distributions without performing regression is presented. Assuming
continuity of the modeling function the variance is given in terms of
conditional probabilities extracted from the data. For $N$ data points
the computational demand is $N^2$.The method is successfully illustrated
with data generated by the Ikeda and Lorentz maps augmented with noise.
As a by-product the embedding dimensions of these maps are extracted.
Comparing the predicted residual errors with those from linear models
provides a signal for nonlinearity.abs.
LU TP 94-19