2012
DOI: 10.1162/neco_a_00225
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Higher-Order Approximations for Testing Neglected Nonlinearity

Abstract: We illustrate the need to use higher-order (specifically sixth-order) expansions in order to properly determine the asymptotic distribution of a standard artificial neural network test for neglected nonlinearity. The test statistic is a quasi-likelihood ratio (QLR) statistic designed to test whether the mean square prediction error improves by including an additional hidden unit with an activation function violating the no-zero condition in Cho, Ishida, and White (2011). This statistic is also shown to be asym… Show more

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Cited by 10 publications
(3 citation statements)
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“…(1) n (0; ) is not necessarily equal to zero and we can apply a central limit theorem (CLT) to this derivative. In the ANN literature, it is common to have zero first-order derivatives, so that higher-order approximations are needed for model approximations (e.g., White, 2011, 2013;and White and Cho, 2012). This difference mainly arises because the nonlinear functions in White (2011, 2013) and White and Cho (2012) have nuisance parameters that are multiplicative to X t , whereas in the present case the nuisance parameter enters through the power coefficient.…”
Section: When Is Not Identifiedmentioning
confidence: 99%
“…(1) n (0; ) is not necessarily equal to zero and we can apply a central limit theorem (CLT) to this derivative. In the ANN literature, it is common to have zero first-order derivatives, so that higher-order approximations are needed for model approximations (e.g., White, 2011, 2013;and White and Cho, 2012). This difference mainly arises because the nonlinear functions in White (2011, 2013) and White and Cho (2012) have nuisance parameters that are multiplicative to X t , whereas in the present case the nuisance parameter enters through the power coefficient.…”
Section: When Is Not Identifiedmentioning
confidence: 99%
“…Cho, Ishida, and White (, ) and White and Cho () examined testing linear model hypotheses by adding an analytic function to the linear model following the framework of Bierens () and Stinchcombe and White (). They showed that higher‐order Taylor expansions are necessary in deriving the null limit distribution of the QLR test statistic.…”
Section: Sequential Qlr Testing For Nonlinearity With Stationary Datamentioning
confidence: 99%
“…In addition to these, higher-order approximations of the quasi-likelihood function can be further simplified if directional derivatives are used. White (2011, 2012) and White and Cho (2012) revisit testing neglected linearity using artificial neural networks and show that its analysis requires higher-order approximations than the conventional analysis.…”
Section: Example 4: Box-cox's (1964) Transformationmentioning
confidence: 99%