# Parameter estimation

• Apr 15th 2011, 08:58 AM
BrownianMan
Parameter estimation
Let X_1,X_2,...,X_n be iid Bernoulli(p). Also let T be Binomial(n, p).

So I found that they both have the same moment generating function, and I found the mean and variance of T. The question asks:

Let n=20 and (x_1+...+x_n)=9. Using the method of moments, find an estimate of theta = log(p/(1-p)).

I'm not sure how to proceed from here.
• Apr 15th 2011, 02:10 PM
theodds
Quote:

Originally Posted by BrownianMan
Let X_1,X_2,...,X_n be iid Bernoulli(p). Also let T be Binomial(n, p).

So I found that they both have the same moment generating function, and I found the mean and variance of T. The question asks:

Let n=20 and (x_1+...+x_n)=9. Using the method of moments, find an estimate of theta = log(p/(1-p)).

I'm not sure how to proceed from here.

With method of moments, the game is to equate the empirical moments with the theoretical moments. Set Xbar = p, then just plug that in to get the estimate of theta.
• Apr 15th 2011, 04:07 PM
BrownianMan
So would the answer be -0.08?
• Apr 15th 2011, 11:23 PM
matheagle
use p-hat as 9/20 to estimate p in theta

ln (.45/.55)
• Apr 18th 2011, 09:55 AM
BrownianMan
Thanks, I got it!

The next part of the question which I'm not sure of is:

Obtain a 95% confidence interval for theta based on the MLE of theta.