next up previous
Next: Rao Test Up: Hypothesis Tests Previous: Hypothesis Tests

Wald Test

A Wald test can be performed with the samples already done to determine the MLE. If the constraints imposed in the null hypothesis are of the form tex2html_wrap_inline4277 and tex2html_wrap_inline4279 , and tex2html_wrap_inline4281 is the (observed or expected) Fisher information, then the Wald test statistic is

displaymath4283

where tex2html_wrap_inline3941 is the MLE in the alternative hypothesis.

In our example, the constraint is simply tex2html_wrap_inline3145 , so tex2html_wrap_inline4289 . So the formula simplifies to

displaymath4291

where tex2html_wrap_inline4293 is the second component of the MLE and tex2html_wrap_inline4295 is the 2,2 component of the inverse Fisher information (1.44). This gives tex2html_wrap_inline4297 .



Charles Geyer
Fri Jul 5 15:26:21 CDT 1996