Abstract
This study examined the extreme learning machine (ELM) applied to the Wald test statistic for the model specification of the conditional mean, which we call the WELM testing procedure. The omnibus test statistics available in the literature weakly converge to a Gaussian stochastic process under the null that the model is correct, and this makes their application inconvenient. By contrast, the WELM testing procedure is straightforwardly applicable when detecting model misspecification. We applied the WELM testing procedure to the sequential testing procedure formed by a set of polynomial models and estimate an approximate conditional expectation. We then conducted extensive Monte Carlo experiments to evaluate the performance of the sequential WELM testing procedure and verify that it consistently estimates the most parsimonious conditional mean when the set of polynomial models contains a correctly specified model. Otherwise, it consistently rejects all the models in the set.
Highlights
Conducting data inference using correctly specified models is desirable for predicting future observations
This table reports the proportion of estimated polynomial degrees using the sequential WELM testing procedure
We applied the Wald test statistic assisted by the extreme learning machine (ELM) to test the correct model assumption and estimate a close approximation of the conditional mean
Summary
Conducting data inference using correctly specified models is desirable for predicting future observations. Baek, Cho, and Phillips [18] note that, if the QLR test statistic in Cho, Ishida, and White [7] is applied to a linear model augmented by a power transformation, the twofold identification problem is transformed into a trifold Davies’ [11,12] identification problem They overcome this and derive the null limit distribution of the QLR test statistic. Cho and Phillips [17] extend the QLR test statistic to test the null of the polynomial function hypothesis and obtain its null limit distribution by overcoming the multifold identification problem, which is further developed from the trifold identification problem in Baek, Cho, and Phillips [18] In addition to this derivation, they apply the null limit distribution to the sequential testing procedure to search for a close approximation of the conditional mean function.
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