Lecture 12. D) Wald Test

From Significant Statistics
Jump to navigation Jump to search

Wald Test

The Wald test statistic is given by


This test can also be motivated as an approximation to the LRT. The principle of the Wald test is to reject the null hypothesis when [math]\left|\widehat{\theta}_{ML}-\theta_{0}\right|[/math] is large.

The denominator is a measure of informativeness of [math]\widehat{\theta}_{ML}[/math]. It increases the rejection rate as the uncertainty over [math]\widehat{\theta}_{ML}[/math] decreases. (If the estimator is more precise, then we reject for lower distances).