# Estimating parameters using a different method?

• Aug 15th 2012, 11:28 PM
arun4
Estimating parameters using a different method?
Hi, I have a probability distribution which has two parameters a and b
I re-parametrized the distribution such that the new distribution has two parameters c and d where
c=a
but
d = 1/b - 1
I can easily estimate a and b but I need to make inferences on c and d, specially d ,
So my question is: If I estimate b and use relationship d=1/b -1 to find out the values of d Is it correct? Is there any information loss?
Also, How can I find the standard errors and confidence intervals of d if those exist for b ?

Thank you very much.
• Sep 8th 2012, 10:08 PM
chiro
Re: Estimating parameters using a different method?
Hey arun4.

If you are using the MLE estimator, you can use what is called the invariance principle to estimate parameters that are functions of a particular random variable.

So lets say you use the MLE estimator for b (call it b_hat). Then if you want to get an estimator for d_hat and you use the MLE estimator to get b_hat then d_hat = f(b_hat) = 1/b_hat - 1 and you're done.

There are also ways of generating intervals for these estimators as well and you might want to get a book on statistical inference.

This is only guaranteed as far as I know for the MLE estimator so don't try and use another one like Method of Moments and do the same thing.
• Sep 14th 2012, 04:24 AM
arun4
Re: Estimating parameters using a different method?
Thank you chiro