Pre-checking for non-monotonicity of the Wald statistic

摘要

The non-monotonic behaviour of the Wald test in some finite-sample applications leads to low power when the null hypothesis needs rejection most. This article proposes a simple check for discerning if the Wald statistic for testing significance of regression coefficients is non-monotonic in the neighbourhood of the parameter space from which the sample data are drawn. Monte Carlo simulations show that this method works rather well for detecting situations where the Wald test can be safely applied. An example is provided to illustrate the use of this check.