Seminars 2009 — Abstracts

Friday, July 24

Speaker: Max King, Monash

Title: A New Procedure for Multiple One-Sided Hypothesis Testing

Abstract: A significant role for hypothesis testing in econometrics is for diagnostic checking of statistical models. In terms of the testing problem that involves multiple test statistics, King, Zhang and Akram (2007) presented a new procedure for multiple testing, which involves estimating the joint density of the vector of multiple test statistics under the null hypothesis through bootstrapping and approximating the p-value using this estimated density through Monte Carlo simulations. They found that when the component tests are invariant to the nuisance parameters, this testing procedure produces higher powers than the conventional tests. Akram, Zhang and King (2008) investigated the application of this testing procedure to the information matrix test, which is an example for the situation where the component tests are only asymptotically invariant to all nuisance parameters. They found that this testing procedure has higher powers than the traditional Chi-square test statistic. According to our experience, one-sided tests tend to have less accurate critical values than two-sided tests when the classical testing approaches are used. As such, we may use larger samples for testing one-sided hypotheses through the testing procedure proposed by King, Zhang and Akram (2007) in order to achieve the same level of accuracy as for two-sided tests. In this paper we apply this new procedure of multiple testing to test the null hypothesis that allows for at least one of the component tests being one-sided. We compare this new testing procedure with the F-test and the joint one-sided test proposed by King and Smith (1986). We find that all tests have approximately correct sizes, while the power of this new testing procedure is higher than that of the other two tests.