MTH-416, REGRESSION ANALYSIS Lecture Notes - Lecture 54: Indian Institute Of Technology Kanpur, Likelihood Ratios In Diagnostic Testing, Likelihood-Ratio Test
6 Apr 2023
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2 are the maximum likelihood estimates of and likelihood function. 2 ( n y x y x exp n. 2( y x y x n y x y x. The constrained likelihood under is (2 ) y x. 0 is known, so the constrained likelihood function has an optimum variance estimator. L n (2 ) (2 ) y x y x. 0 y x y x is the ratio of the quadratic forms. Now we simplify the numerator in as follows: y x. Now we find the distribution of the quadratic forms involved is. )n n n matrix of rank, p then. If b is another n n symmetric idempotent matrix of rank q , then. So using this result, we have y hy. 25 25 25 and we have the numerator in. X where h is an idempotent matrix with rank k . Furthermore, the product of the quadratic form matrices in the numerator ( of.
