is random sample from Rayleigh distribution
1. Show that and than construct unbiased estimator of parameter based on
2. Estimate parameter from following observations:
---Code:16.88 10.23 4.59 6.66 13.68 14.23 19.87 9.40 6.51 10.95
1. I have just plugged in 2 theta in Rayleigh's variance formula and it evaluates to true, but I'm not sure about correct way of constructing unbiased estimator
2. I need help with this one
An estimate is unbiased if its expected value is equal to the true value of the parameter being estimated. So, you can confirm the estimate is unbiased by taking its expectation.
So, assuming your estimate was
And the estimator is unbiased.
I have been told, but i never managed to prove, that all method of moments estimates are unbiased and you dont need to check each time. But im not convinced...
Guys, what am I missing here? I ran monte carlo simulations for Rayleigh samples and this estimator does not come close for small n. For example, with sigma = 1.0, using sample sizes of 2 the average value of the estimate is 0.50 (over 1MM iterations). Even with sample sizes of 10 the estimate is still only .90! Shouldn't an unbiased estimator work better than this for small n?