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Closed-loop Neuro-robotic Experiments to Test Computational Properties of Neuronal Networks
11:18

Closed-loop Neuro-robotic Experiments to Test Computational Properties of Neuronal Networks

Published on: March 2, 2015

Revisiting tests for neglected nonlinearity using artificial neural networks.

Jin Seo Cho1, Isao Ishida, Halbert White

  • 1School of Economics, Yonsei University, Seoul 120-749, Korea. jinseocho@yonsei.ac.kr

Neural Computation
|February 9, 2011
PubMed
Summary
This summary is machine-generated.

This study analyzes artificial neural network (ANN) based regression tests for nonlinearity. We derive the asymptotic null distribution, finding the previous results hold under stronger conditions, crucial for accurate statistical inference.

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Last Updated: Jun 4, 2026

Closed-loop Neuro-robotic Experiments to Test Computational Properties of Neuronal Networks
11:18

Closed-loop Neuro-robotic Experiments to Test Computational Properties of Neuronal Networks

Published on: March 2, 2015

Area of Science:

  • Statistics
  • Machine Learning
  • Econometrics

Background:

  • Artificial neural networks (ANNs) offer powerful tools for modeling complex nonlinear relationships in regression analysis.
  • Existing ANN-based tests for neglected nonlinearity have limitations in understanding their asymptotic behavior.
  • The null hypothesis of regression linearity can be approached through different components, requiring careful analysis.

Purpose of the Study:

  • To analyze the asymptotic null distribution of a convenient ANN-based quasi-likelihood ratio statistic for testing neglected nonlinearity.
  • To investigate the interaction between the two components of the null hypothesis.
  • To establish the conditions under which existing asymptotic results remain valid.

Main Methods:

  • Derivation of the asymptotic null distribution for an ANN-based quasi-likelihood ratio statistic.
  • Separate analysis of the two components of the null hypothesis of regression linearity.
  • Monte Carlo simulations to corroborate theoretical findings and assess practical implications.

Main Results:

  • The previously known asymptotic null distribution for type 1 cases is confirmed, but under stricter regularity conditions.
  • The interaction between the null components was analyzed, clarifying the overall asymptotic behavior.
  • Simulations demonstrated that standard methods can lead to misleading results when new, stronger conditions are not met.

Conclusions:

  • The study provides a more robust theoretical foundation for ANN-based nonlinearity tests.
  • Understanding and satisfying the identified stronger regularity conditions are essential for reliable statistical inference.
  • Violations of these conditions can compromise the validity of standard statistical methods in practice.