Sequentially Estimating the Approximate Conditional Mean Using Extreme Learning Machines |
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Authors: | Lijuan Huo Jin Seo Cho |
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Institution: | 1.School of Humanities and Social Sciences, Beijing Institute of Technology, Haidian, Beijing 100081, China;2.School of Economics, Yonsei University, Seodaemun, Seoul 03722, Korea |
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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. |
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Keywords: | conditional mean specification testing omnibus test gaussian process extreme learning machine wald test statistic functional regression sequential testing procedure consistent correct model estimation |
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