Suppose that X1,...,Xn form a random sample

Chapter 8, Problem 10

(choose chapter or problem)

Get Unlimited 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 .

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

Add to cart


Study Tools You Might Need

Not The Solution You Need? Search for Your Answer Here:

×

Login

Login or Sign up for access to all of our study tools and educational content!

Forgot password?
Register Now

×

Register

Sign up for access to all content on our site!

Or login if you already have an account

×

Reset password

If you have an active account we’ll send you an e-mail for password recovery

Or login if you have your password back