My question is motivated by a problem with estimation by maximum likelihood. In simple terms, I want to estimate a parameter and have three variables, , and , such that . Using all three variables is pointless and the joint pdf is singular. Now, suppose that instead of I have such that , where is independent from and and its distribution does not depend on . The joint pdf of , and is not singular. Seems to me obvious that does not contain any additional information about , given and . So, I think it must be true that, in terms of the likelihood function, . If I am correct, what would be the best way to prove it? Thanks.
Last edited by Sam Vimes; 07-18-2014 at 01:29 PM. Reason: to textify
Sam Vimes (07-18-2014)
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