Sequentially estimating the approximate conditional mean using extreme learning machines

Lijuan Huo, Jin Seo Cho

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Article number1294
Pages (from-to)1-21
Number of pages21
Issue number11
Publication statusPublished - 2020 Nov

Bibliographical note

Publisher Copyright:
© 2020 by the authors. Licensee MDPI, Basel, Switzerland.

All Science Journal Classification (ASJC) codes

  • Information Systems
  • Mathematical Physics
  • Physics and Astronomy (miscellaneous)
  • Electrical and Electronic Engineering


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