Testing for Neglected Nonlinearity Using Extreme Learning Machines

Shin, Kyu Lee; Cho, Jin Seo

doi:10.1142/s0218488513400205

Cited by 2 publications

(1 citation statement)

References 18 publications

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“…, X m n,1 } for m = 3, 5. Here, L (1) n (0; λ) = 0 and L (2) n (0; λ) = 0, whereas Cho et al's (2011) no-zero condition gives L (1) n (0; λ) = 0 and L (2) n (0; λ) = 0. This permits them to use L (2) n (0; λ) as the key term determining the asymptotic distribution, but this is not possible here.…”

Section: A Qlr Test For Neglected Nonlinearitymentioning

confidence: 99%

Higher-Order Approximations for Testing Neglected Nonlinearity

White

Cho

2012

Neural Computation

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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 asymptotically equivalent under the null to the Lagrange multiplier (LM) statistic of Luukkonen, Saikkonen, and Teräsvirta (1988) and Teräsvirta (1994). In addition, we compare the power properties of our QLR test to one satisfying the no-zero condition and find that the latter is not consistent for detecting a DGP with neglected nonlinearity violating an analogous no-zero condition, whereas our QLR test is consistent.

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Section: A Qlr Test For Neglected Nonlinearitymentioning

confidence: 99%

Higher-Order Approximations for Testing Neglected Nonlinearity

White

Cho

2012

Neural Computation

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Testing a constant mean function using functional regression

Cho,

Huang,

White

2023

Neural Comput & Applic

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In this paper, we study functional regression and its properties in testing the hypothesis of a constant zero mean function or an unknown constant non-zero mean function. As we show, the associated Wald test statistics have standard chi-square limiting null distributions, standard non-central chi-square distributions for local alternatives converging to zero at a √ n rate, and are consistent against global alternatives. These properties permit computationally convenient tests of hypotheses involving nuisance parameters. In particular, we develop new alternatives to tests for mixture distributions and for regression misspecification, both of which involve nuisance parameters identified only under the alternative. In Monte Carlo studies, we find that our tests have well behaved levels. We find that the new procedures may sacrifice only a modest amount of power compared to procedures like those of Davies (1987), which fully exploit the covariance structure of the Gaussian processes underlying our statistics. Further, functional regression tests can have power better than existing methods that do not exploit this covariance structure, like the specification testing procedures of Bierens (1982Bierens ( , 1990 or Stinchcombe and White (1998).

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Testing for Neglected Nonlinearity Using Extreme Learning Machines

Cited by 2 publications

References 18 publications

Higher-Order Approximations for Testing Neglected Nonlinearity

Higher-Order Approximations for Testing Neglected Nonlinearity

Testing a constant mean function using functional regression

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