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Determining Dependency Structures And Estimating Nonlinear Regression Errors Without Doing Regression

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  • CARSTEN PETERSON

    (Department, of Theoretical Physics, University of Lund, Sölvegatan 14A S-223 62 Lund, Sweden)

Abstract

A general method is discussed, the δ-test, which establishes functional dependencies given a table of measurements. The approach is based on calculating conditional probabilities from data densities. Imposing the requirement of continuity of the underlying function the obtained values of the conditional probabilities carry information on the variable dependencies. The power of the method is illustrated on synthetic time-series with different time-lag dependencies and noise levels. ForNdata points the computational demand isN2. Also, the same method is used for estimating nonlinear regression errors and their distributions without performing regression. Comparing the predicted residual errors with those from linear models provides a signal for nonlinearity. The virtue of the method in the context of feedforward neural networks is stressed with respect to preprocessing data and tracking residual errors.

Suggested Citation

  • Carsten Peterson, 1995. "Determining Dependency Structures And Estimating Nonlinear Regression Errors Without Doing Regression," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 6(04), pages 611-616.
    • Handle: RePEc:wsi:ijmpcx:v:06:y:1995:i:04:n:s0129183195000514
    DOI: 10.1142/S0129183195000514
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