Sequentially Estimating Approximate Conditional Mean Using the Extreme Learning Machine

This study applies the Wald test statistic assisted by the extreme learning machine (ELM) to test for model misspecification. When testing for model misspecification of conditional mean, the omnibus test statistics weakly converge to a Gaussian stochastic process under the null that makes their application inconvenient. We overcome this by applying the ELM to the Wald test statistic defined by the functional regression and also apply it to a sequential testing procedure to estimate an approximate conditional expectation. By conducting extensive Monte Carlo experiments, we evaluate its performance and verify that the sequential WELM testing procedure estimates the most parsimonious conditional mean equation consistently if the candidate polynomial models are correctly specified; and further it consistently rejects all candidate models if all of them are misspecified.