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Math Help - Estimating parameters using a different method?

  1. #1
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    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.
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  2. #2
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    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.
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  3. #3
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    Re: Estimating parameters using a different method?

    Thank you chiro
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