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Estimating nonlinear regression errors without doing regression

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  • Hong Pi
  • 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 N2. Comparing the predicted residual errors with those derived from a linear model assumption provides a signal for nonlinearity. The method is successfully illustrated with data generated by the Ikeda and Lorenz maps augmented with noise. As a by-product the embedding dimensions of these maps are also extracted.

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  • Hong Pi & Carsten Peterson, 2014. "Estimating nonlinear regression errors without doing regression," Papers 1404.3219, arXiv.org.
    • Handle: RePEc:arx:papers:1404.3219
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    File URL: http://arxiv.org/pdf/1404.3219
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