Cramer Rao problem - Math Help Forum

$Math Help Forum$

$Go Back$		Math Help Forum > University Math Help > Advanced Probability and Statistics
$Reload this Page$ Cramer Rao problem

Download MHF Flyer

Mark Forums Read

$Reply$

#1

$Old$ November 5th, 2009, 11:00 PM

pengchao1024 $pengchao1024 is offline$

Junior Member

Join Date: May 2008

Posts: 31

Country:

United States

Thanks: 0

Thanked 0 Times in 0 Posts

$pengchao1024 is on a distinguished road$

$Default$ Cramer Rao problem

$cramer-rao-problem-2009-11-06-05.47.22.png幕快照 2009-11-06 上午05.47.22.png Views: 5 Size: 37.8 KB ID: 13708$

i found:

$E(\widetilde{\theta})=\theta+\frac{1}{n} \ \ \ \ \ var(\widetilde{\theta})=\frac{1}{n^{2}}$

so i guess we need n goes to infinity to make theta an unbiased estimator.

what about the last two questions

$Reply With Quote$

Advertisement

#2

$Old$ November 5th, 2009, 11:45 PM

$matheagle's Avatar$

matheagle $matheagle is online now$

MHF Contributor

Join Date: Feb 2009

Posts: 1,367

Country:

United States

Thanks: 99

Thanked 560 Times in 503 Posts

$matheagle is a splendid one to behold$ $matheagle is a splendid one to behold$ $matheagle is a splendid one to behold$ $matheagle is a splendid one to behold$ $matheagle is a splendid one to behold$ $matheagle is a splendid one to behold$ $matheagle is a splendid one to behold$

$Default$

What is this $\widetilde{\theta}$ ?

The MLE of $\theta$ is the smallest order statistic.

$Reply With Quote$

#3

$Old$ November 5th, 2009, 11:47 PM

pengchao1024 $pengchao1024 is offline$

Junior Member

Join Date: May 2008

Posts: 31

Country:

United States

Thanks: 0

Thanked 0 Times in 0 Posts

$pengchao1024 is on a distinguished road$

$Default$ rep

$\widetilde{\theta}$ is MLE of theta

$Reply With Quote$

#4

$Old$ November 5th, 2009, 11:54 PM

$matheagle's Avatar$

matheagle $matheagle is online now$

MHF Contributor

Join Date: Feb 2009

Posts: 1,367

Country:

United States

Thanks: 99

Thanked 560 Times in 503 Posts

$matheagle is a splendid one to behold$ $matheagle is a splendid one to behold$ $matheagle is a splendid one to behold$ $matheagle is a splendid one to behold$ $matheagle is a splendid one to behold$ $matheagle is a splendid one to behold$ $matheagle is a splendid one to behold$

$Default$

and what is the MLE here?

It's the smallest order stat.

$Reply With Quote$

#5

$Old$ November 5th, 2009, 11:58 PM

pengchao1024 $pengchao1024 is offline$

Junior Member

Join Date: May 2008

Posts: 31

Country:

United States

Thanks: 0

Thanked 0 Times in 0 Posts

$pengchao1024 is on a distinguished road$

$Default$ wt

wat is that? i never heard of it

$Reply With Quote$

#6

$Old$ November 6th, 2009, 12:02 AM

$matheagle's Avatar$

matheagle $matheagle is online now$

MHF Contributor

Join Date: Feb 2009

Posts: 1,367

Country:

United States

Thanks: 99

Thanked 560 Times in 503 Posts

$matheagle is a splendid one to behold$ $matheagle is a splendid one to behold$ $matheagle is a splendid one to behold$ $matheagle is a splendid one to behold$ $matheagle is a splendid one to behold$ $matheagle is a splendid one to behold$ $matheagle is a splendid one to behold$

$Default$

If this problem was assigned, then your teacher should have covered order stats. This is just the minimum of the data in this case.

Order statistic - Wikipedia, the free encyclopedia

$Reply With Quote$

#7

$Old$ November 6th, 2009, 12:20 AM

pengchao1024 $pengchao1024 is offline$

Junior Member

Join Date: May 2008

Posts: 31

Country:

United States

Thanks: 0

Thanked 0 Times in 0 Posts

$pengchao1024 is on a distinguished road$

$Default$ yea

yeah. i know the MLE. but wat about the last two questions?

$Reply With Quote$

#8

$Old$ November 6th, 2009, 12:26 AM

$matheagle's Avatar$

matheagle $matheagle is online now$

MHF Contributor

Join Date: Feb 2009

Posts: 1,367

Country:

United States

Thanks: 99

Thanked 560 Times in 503 Posts

$matheagle is a splendid one to behold$ $matheagle is a splendid one to behold$ $matheagle is a splendid one to behold$ $matheagle is a splendid one to behold$ $matheagle is a splendid one to behold$ $matheagle is a splendid one to behold$ $matheagle is a splendid one to behold$

$Default$

nevermind

Last edited by matheagle; November 6th, 2009 at 01:36 PM.

$Reply With Quote$

#9

$Old$ November 6th, 2009, 01:01 AM

pengchao1024 $pengchao1024 is offline$

Junior Member

Join Date: May 2008

Posts: 31

Country:

United States

Thanks: 0

Thanked 0 Times in 0 Posts

$pengchao1024 is on a distinguished road$

$Default$ know

i know it. but i dont know it is called that.

$Reply With Quote$

$Reply$

« (Cumulative) Probability Density Functions | Top | Quantiles/Order Statistics »

Thread Tools
$Show Printable Version$ Show Printable Version $Email this Page$ Email this Page
Display Modes
$Linear Mode$ Linear Mode $Hybrid Mode$ Switch to Hybrid Mode $Threaded Mode$ Switch to Threaded Mode

Posting Rules
You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is Off Trackbacks are Off Pingbacks are Off Refbacks are Off

Forum Jump

All times are GMT -7. The time now is 12:46 AM.

your link here Sponsors

rv solar, e-learning,

Math Help Forum is a community of maths forums with an emphasis on maths help in all levels of mathematics.
Register to post your math questions or just hang out and try some of our math games or visit the arcade.