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Thread: finding the MLE

  1. #1
    Junior Member
    May 2010

    finding the MLE

    I have a question about finding the MLE..

    $\displaystyle Let\;\; $X_1, \cdots, X_n$ \mbox{be a random sample from a population with pdf}\;\;$f_{\theta}(x)=(\theta+1)x^{\theta}$
    $\displaystyle ;\;0<x<1;\;\mbox{where }\theta>-1$ \mbox{is an unknown parameter}.$

    Find the MLE for $\displaystyle e^{\theta}$

    I am confused on how to start this. To find the MLE of $\displaystyle \theta$, we would find the likelihood function of $\displaystyle L(\theta|x)$. so does this mean the to find the MLE for the MLE for $\displaystyle e^{\theta}$, I would go like this:

    $\displaystyle L(e^{\theta}|x)= \prod_{i=1}^n (e^{\theta}+1){x_i}^{e^{\theta}}$

    is this right??
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  2. #2
    MHF Contributor harish21's Avatar
    Feb 2010
    Dirty South
    Are you familiar with the Invariance Property of the MLEs?
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