Mixing
Find the UMVUE of $b^{mu}$
$begingroup$
Let $X_1,X_2,..X_n$ be a random sample from Cauchy$(mu,1)$ population.
Find the UMVUE of $b^{mu}$ where $b$ is any positive real number.
Now actually calculating sample mean won't work here because its distribution is also Cauchy$(mu,1)$,so expectation won't exist.And all I know is that the sample median asymptotically goes to $mu$,so it won't work here either.Is there any trick other than the normal procedures like Lehmann Scheffe to do this?
probability probability-theory probability-distributions statistical-inference parameter-estimation
asked Jan 29 at 2:50
Legend KillerLegend Killer
1,6721624
$endgroup$
add a comment |
$begingroup$
Let $X_1,X_2,..X_n$ be a random sample from Cauchy$(mu,1)$ population.
Find the UMVUE of $b^{mu}$ where $b$ is any positive real number.
Now actually calculating sample mean won't work here because its distribution is also Cauchy$(mu,1)$,so expectation won't exist.And all I know is that the sample median asymptotically goes to $mu$,so it won't work here either.Is there any trick other than the normal procedures like Lehmann Scheffe to do this?
probability probability-theory probability-distributions statistical-inference parameter-estimation
asked Jan 29 at 2:50
Legend KillerLegend Killer
1,6721624
$endgroup$
$begingroup$
I don't know, is the sample $X_1,ldots,X_n$ a complete statistic? (It is trivially sufficient of course)
$endgroup$
– StubbornAtom
Jan 29 at 6:54
$begingroup$
What is $u$? The sample mean $frac1n sum X_i$?
$endgroup$
– Lee David Chung Lin
Jan 31 at 3:42
add a comment |
$begingroup$
Let $X_1,X_2,..X_n$ be a random sample from Cauchy$(mu,1)$ population.
Find the UMVUE of $b^{mu}$ where $b$ is any positive real number.
Now actually calculating sample mean won't work here because its distribution is also Cauchy$(mu,1)$,so expectation won't exist.And all I know is that the sample median asymptotically goes to $mu$,so it won't work here either.Is there any trick other than the normal procedures like Lehmann Scheffe to do this?
probability probability-theory probability-distributions statistical-inference parameter-estimation
asked Jan 29 at 2:50
Legend KillerLegend Killer
1,6721624
$endgroup$
Let $X_1,X_2,..X_n$ be a random sample from Cauchy$(mu,1)$ population.
Find the UMVUE of $b^{mu}$ where $b$ is any positive real number.
Now actually calculating sample mean won't work here because its distribution is also Cauchy$(mu,1)$,so expectation won't exist.And all I know is that the sample median asymptotically goes to $mu$,so it won't work here either.Is there any trick other than the normal procedures like Lehmann Scheffe to do this?
probability probability-theory probability-distributions statistical-inference parameter-estimation
probability probability-theory probability-distributions statistical-inference parameter-estimation
asked Jan 29 at 2:50
Legend KillerLegend Killer
1,6721624
asked Jan 29 at 2:50
Legend KillerLegend Killer
1,6721624
asked Jan 29 at 2:50
Legend KillerLegend Killer
1,6721624
asked Jan 29 at 2:50
Legend KillerLegend Killer
1,6721624
asked Jan 29 at 2:50
Legend KillerLegend Killer
1,6721624
1,6721624
$begingroup$
I don't know, is the sample $X_1,ldots,X_n$ a complete statistic? (It is trivially sufficient of course)
$endgroup$
– StubbornAtom
Jan 29 at 6:54
$begingroup$
What is $u$? The sample mean $frac1n sum X_i$?
$endgroup$
– Lee David Chung Lin
Jan 31 at 3:42
add a comment |
$begingroup$
I don't know, is the sample $X_1,ldots,X_n$ a complete statistic? (It is trivially sufficient of course)
$endgroup$
– StubbornAtom
Jan 29 at 6:54
$begingroup$
What is $u$? The sample mean $frac1n sum X_i$?
$endgroup$
– Lee David Chung Lin
Jan 31 at 3:42
$begingroup$
I don't know, is the sample $X_1,ldots,X_n$ a complete statistic? (It is trivially sufficient of course)
$endgroup$
– StubbornAtom
Jan 29 at 6:54
$begingroup$
I don't know, is the sample $X_1,ldots,X_n$ a complete statistic? (It is trivially sufficient of course)
$endgroup$
– StubbornAtom
Jan 29 at 6:54
$begingroup$
What is $u$? The sample mean $frac1n sum X_i$?
$endgroup$
– Lee David Chung Lin
Jan 31 at 3:42
$begingroup$
What is $u$? The sample mean $frac1n sum X_i$?
$endgroup$
– Lee David Chung Lin
Jan 31 at 3:42
add a comment |
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$begingroup$
I don't know, is the sample $X_1,ldots,X_n$ a complete statistic? (It is trivially sufficient of course)
$endgroup$
– StubbornAtom
Jan 29 at 6:54
$begingroup$
What is $u$? The sample mean $frac1n sum X_i$?
$endgroup$
– Lee David Chung Lin
Jan 31 at 3:42