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Suppose that X1,...,Xn form a random sample
Chapter 8, Problem 10(choose chapter or problem)
Suppose that X1,...,Xn form a random sample from the normal distribution with mean 0 and unknown standard deviation > 0. Find the lower bound specified by the information inequality for the variance of any unbiased estimator of log .
Questions & Answers
QUESTION:
Suppose that X1,...,Xn form a random sample from the normal distribution with mean 0 and unknown standard deviation > 0. Find the lower bound specified by the information inequality for the variance of any unbiased estimator of log .
ANSWER:Step 1 of 4
Cramer-Rao Inequality
Suppose that form a random sample from a distribution for which the p.d.f. is . Let be a statistic with finite variance. Let . We assume that is a differentiable function of . Then
There will be equality in above expression if and only if there exist functions and that may be depend on but not depend on and satisfy the relation