Score Test - Multiple Parameters

Multiple Parameters

A more general score test can be derived when there is more than one parameter. Suppose that is the maximum likelihood estimate of under the null hypothesis . Then

$U^T(\hat{\theta}_0) I^{-1}(\hat{\theta}_0) U(\hat{\theta}_0) \sim \chi^2_k$

asymptotically under, where is the number of constraints imposed by the null hypothesis and

$U(\hat{\theta}_0) = \frac{\partial \log L(\hat{\theta}_0 | x)}{\partial \theta}$

and

$I(\hat{\theta}_0) = -E\left(\frac{\partial^2 \log L(\hat{\theta}_0 | x)}{\partial \theta \partial \theta'} \right).$

This can be used to test .

Famous quotes containing the words multiple and/or parameters:

“Creativity seems to emerge from multiple experiences, coupled with a well-supported development of personal resources, including a sense of freedom to venture beyond the known.”
—Loris Malaguzzi (20th century)

“What our children have to fear is not the cars on the highways of tomorrow but our own pleasure in calculating the most elegant parameters of their deaths.”
—J.G. (James Graham)