Question: F-test as a likelihood ratio test. Consider the Gaussian linear model and let H be an r-dimensional hypothesis space. Show that the likelihood ratio R

F-test as a likelihood ratio test. Consider the Gaussian linear model and let H be an r-dimensional hypothesis space. Show that the likelihood ratio R D sup

;vW A 62H

A ;vE

sup

;vW A 2H

A ;vE is an increasing function of the statistic FH;L from (12.18), namely R D .1C sr ns FH;L/n=2.

Conclude that Fisher’s F -test is a likelihood ratio test.

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