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CRLB Question
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Zootal
Nov 9, 2009, 11:14:18 PM11/9/09
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I'm finding the CRLB on estimator variance for any unbiased estimater of
theta, and I have an expression describing it's density function, f.
theta, and I have an expression describing it's density function, f.
The FIM is the expected value of [ d/d(theta) ln(f)]^2. So I do the math for
[d/d(theta) ln(f) ]^2 and I get an answer I'm happy with, say 2/(1+theta).
Question - The FIM is the expected value of [ 2/(1+theta)]. How do I get the
expected value of this expression? I'm not quite sure how to finish this
problem.
Jack Tomsky
Nov 10, 2009, 12:43:57 AM11/10/09
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Since 2/(1+theta) is the same for all samples x1, ..., xn, its expected value is 2/(1+theta), which is the Cramer-Rao lower bound for the asymptotic variance.
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