The Wald test is a large-sample statistical test of restrictions on an unknown parameter using the distance between an unrestricted
estimator and the value specified by the null
hypothesis. For a scalar parameter 
, the Wald statistic for testing 
is
 |
where 
is the estimated standard
error of 
.
Under standard regularity conditions and the null hypothesis, 
converges in distribution to a chi-squared
distribution with one degree of freedom. More generally, a joint Wald test of
independent smooth restrictions has an
asymptotic chi-squared distribution with
degrees of freedom.
