Testing for Neglected Nonlinearity Using Twofold Unidentified Models under the Null and Hexic Expansions
AbstractWe revisit the twofold identification problem discussed by Cho, Ishida, and White (Neural Computation, 2011), which arises when testing for neglected nonlinearity by artificial neural networks. We do not use the so-called ¡°no-zero¡± condition and employ a sixth-order expansion to obtain the asymptotic null distribution of the quasi-likelihood ratio (QLR) test. In particular, we avoid restricting the number of explanatory variables in the activation function by using the distance and direction method discussed in Cho and White (Neural Computation, 2012). We find that the QLR test statistic can still be used to handle the twofold identification problem appropriately under the set of mild regularity conditions provided here, so that the asymptotic null distribution can be obtained in a manner similar to that in Cho, Ishida, and White (Neural Computation, 2011). This also implies that the weighted bootstrap in Hansen (Econometrica, 1996) can be successfully exploited when testing the linearity hypothesis using the QLR test.
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Bibliographic InfoPaper provided by Yonsei University, Yonsei Economics Research Institute in its series Working papers with number 2013rwp-55.
Length: 31 pages
Date of creation: Feb 2013
Date of revision:
Artificial neural networks; Neglected nonlinearity; Quasi-likelihood ratio test; Distance and direction approach; Gaussian stochastic process; Twofold identification problem; Sixth-order (hexic) expansion; Weighted bootstrap;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2013-03-09 (All new papers)
- NEP-CMP-2013-03-09 (Computational Economics)
- NEP-ORE-2013-03-09 (Operations Research)
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- Donald W.K. Andrews, 1999.
"Testing When a Parameter Is on the Boundary of the Maintained Hypothesis,"
Cowles Foundation Discussion Papers
1229, Cowles Foundation for Research in Economics, Yale University.
- Andrews, Donald W K, 2001. "Testing When a Parameter Is on the Boundary of the Maintained Hypothesis," Econometrica, Econometric Society, vol. 69(3), pages 683-734, May.
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