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Score Statistic of a Binomial Distribution

+2 votes
asked Aug 24, 2016 in STA 2004F - Statistical Theory and Inference by DanNewton (970 points)
recategorized Mar 1, 2017 by Rowan

Hello, my question is related to the score statistic of a binomial distribution.

The book does it by finding var(U), subbing in U, and then solving with the knowledge that Y =n*pi*(1-pi), which I understand.

I tried another method, using var(U) = E(U^2). To do this I subbed in U^2 and solved. This did not give me the same answer and I have tried multiple times. Can I not do it this way?

Edit: I'm now looking directly at the score function:

 $$ U^2=a(y)^2b'(theta)^2+c'(theta)^2+2a(y)b'(theta)c'(theta) $$


$$ E[U^2] = E[a(y)^2]b'(theta)^2+c'(theta)^2+2E[a(y)] b'(theta)c'(theta) $$

Subbing in E[a(Y)]:

$$ = E[a(y)^2]b'(theta)^2-c'(theta)^2 $$

Which is var(U) + an extra term. What is wrong with this calculation?

Edit2: Nevermind, I went wrong in the calc :)

commented Sep 1, 2016 by Richard van Gysen (3,180 points)

Suh dude           

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