Mixing
UMVUE of $theta$ when $X_1,ldots,X_n$ are i.i.d with pdf $f(x)=frac{(lntheta)theta^x }{theta -1}$
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I'm having some trouble finding the UMVU estimator of $theta$ for the following distribution
$$f(x)=frac{(lntheta)theta^x }{theta -1} text{ for } x in (0,1)$$
Specifically, I know $T_n=sum x_i$ is a sufficient complete statistics, but I cannot find an unbiased estimator that is function of $T_n$ nor the MVE estimator. (I actually have trouble even in finding any unbiased estimator of $theta$, so that I cannot use Rao Blackwell theorem).
Thank you for your help.
statistics statistical-inference parameter-estimation
edited Jan 22 at 16:53
StubbornAtom
6,16811339
asked Jan 22 at 16:13
franzkfranzk
1435
$endgroup$
add a comment |
$begingroup$
I'm having some trouble finding the UMVU estimator of $theta$ for the following distribution
$$f(x)=frac{(lntheta)theta^x }{theta -1} text{ for } x in (0,1)$$
Specifically, I know $T_n=sum x_i$ is a sufficient complete statistics, but I cannot find an unbiased estimator that is function of $T_n$ nor the MVE estimator. (I actually have trouble even in finding any unbiased estimator of $theta$, so that I cannot use Rao Blackwell theorem).
Thank you for your help.
statistics statistical-inference parameter-estimation
edited Jan 22 at 16:53
StubbornAtom
6,16811339
asked Jan 22 at 16:13
franzkfranzk
1435
$endgroup$
$begingroup$
Not sure if an unbiased estimator of $theta$ is available in elementary form in this case.
$endgroup$
– StubbornAtom
Jan 22 at 19:15
$begingroup$
Thank you! I did expect it to exist in elementary form since this exercise was given in an exam, but now I'm not sure anymore.
$endgroup$
– franzk
Jan 23 at 15:31
add a comment |
$begingroup$
I'm having some trouble finding the UMVU estimator of $theta$ for the following distribution
$$f(x)=frac{(lntheta)theta^x }{theta -1} text{ for } x in (0,1)$$
Specifically, I know $T_n=sum x_i$ is a sufficient complete statistics, but I cannot find an unbiased estimator that is function of $T_n$ nor the MVE estimator. (I actually have trouble even in finding any unbiased estimator of $theta$, so that I cannot use Rao Blackwell theorem).
Thank you for your help.
statistics statistical-inference parameter-estimation
edited Jan 22 at 16:53
StubbornAtom
6,16811339
asked Jan 22 at 16:13
franzkfranzk
1435
$endgroup$
I'm having some trouble finding the UMVU estimator of $theta$ for the following distribution
$$f(x)=frac{(lntheta)theta^x }{theta -1} text{ for } x in (0,1)$$
Specifically, I know $T_n=sum x_i$ is a sufficient complete statistics, but I cannot find an unbiased estimator that is function of $T_n$ nor the MVE estimator. (I actually have trouble even in finding any unbiased estimator of $theta$, so that I cannot use Rao Blackwell theorem).
Thank you for your help.
statistics statistical-inference parameter-estimation
statistics statistical-inference parameter-estimation
edited Jan 22 at 16:53
StubbornAtom
6,16811339
asked Jan 22 at 16:13
franzkfranzk
1435
edited Jan 22 at 16:53
StubbornAtom
6,16811339
asked Jan 22 at 16:13
franzkfranzk
1435
edited Jan 22 at 16:53
StubbornAtom
6,16811339
edited Jan 22 at 16:53
StubbornAtom
6,16811339
edited Jan 22 at 16:53
StubbornAtom
6,16811339
6,16811339
asked Jan 22 at 16:13
franzkfranzk
1435
asked Jan 22 at 16:13
franzkfranzk
1435
asked Jan 22 at 16:13
franzkfranzk
1435
1435
$begingroup$
Not sure if an unbiased estimator of $theta$ is available in elementary form in this case.
$endgroup$
– StubbornAtom
Jan 22 at 19:15
$begingroup$
Thank you! I did expect it to exist in elementary form since this exercise was given in an exam, but now I'm not sure anymore.
$endgroup$
– franzk
Jan 23 at 15:31
add a comment |
$begingroup$
Not sure if an unbiased estimator of $theta$ is available in elementary form in this case.
$endgroup$
– StubbornAtom
Jan 22 at 19:15
$begingroup$
Thank you! I did expect it to exist in elementary form since this exercise was given in an exam, but now I'm not sure anymore.
$endgroup$
– franzk
Jan 23 at 15:31
$begingroup$
Not sure if an unbiased estimator of $theta$ is available in elementary form in this case.
$endgroup$
– StubbornAtom
Jan 22 at 19:15
$begingroup$
Not sure if an unbiased estimator of $theta$ is available in elementary form in this case.
$endgroup$
– StubbornAtom
Jan 22 at 19:15
$begingroup$
Thank you! I did expect it to exist in elementary form since this exercise was given in an exam, but now I'm not sure anymore.
$endgroup$
– franzk
Jan 23 at 15:31
$begingroup$
Thank you! I did expect it to exist in elementary form since this exercise was given in an exam, but now I'm not sure anymore.
$endgroup$
– franzk
Jan 23 at 15:31
add a comment |
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$begingroup$
Not sure if an unbiased estimator of $theta$ is available in elementary form in this case.
$endgroup$
– StubbornAtom
Jan 22 at 19:15
$begingroup$
Thank you! I did expect it to exist in elementary form since this exercise was given in an exam, but now I'm not sure anymore.
$endgroup$
– franzk
Jan 23 at 15:31