Timeline for How to show unbiased estimator of combination of bernoulli and normal variables?
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 12, 2013 at 2:05 | history | edited | Jeromy Anglim | CC BY-SA 3.0 |
tried to improve title
|
| Jun 13, 2012 at 23:29 | vote | accept | David | ||
| Feb 13, 2012 at 13:24 | comment | added | Xi'an | @David: the question is not worded properly, it should state "is an unbiased estimator of $0$", not "is an unbiased estimator of $\theta$". | |
| Feb 13, 2012 at 12:38 | comment | added | David | @Xi'an, in question a) the condition to prove the unbiasness is $E[\psi(\theta;(X,Y))] = 0$. So proving this is enough for the question and this can be shown by using $E[Y] = \theta^2$ and $E[X] = \theta$. We don't need any estimator, just prove the condition. | |
| Feb 13, 2012 at 8:19 | comment | added | Xi'an | Question a) certainly is absurd as stated: if $\mathbb{E}[\Psi(\theta;(X,Y))]=0$, $\Psi(\theta;(X,Y))$ cannot be unbiased. It can neither be an estimate since it depends on $\theta$! | |
| Feb 13, 2012 at 4:04 | comment | added | David | b)It looks the estimator $\hat\theta = \frac{\sum_{i=1}^nY_i}{\sum_{i=1}^nX_i}$. Now what is the expectation of $\hat\theta$? that is, is $\hat\theta$ unbaised for $\theta$?. How can I find the expectation of $\frac{\sum_{i=1}^nY_i}{\sum_{i=1}^nX_i}$? | |
| Feb 13, 2012 at 4:01 | answer | added | Macro | timeline score: 4 | |
| Feb 13, 2012 at 2:47 | comment | added | David | @ Macro, Yes I missed some information. In a) there should be the condition "An estimator is unbaised if $E[\psi(\theta;(X,Y))] = 0$ and I got the solution using $E[Y] = \theta^2$ and $E[X]= \theta$. Now I want to know the idea of the question b). | |
| Feb 13, 2012 at 1:55 | comment | added | Macro | Is this missing something? What exactly is the estimator? $\psi$ is a function of $\theta$, so it is not the estimator (as the question suggests). Is the estimator the minimizer of $\psi$? | |
| Feb 12, 2012 at 22:53 | history | edited | cardinal |
edited tags
|
|
| Feb 12, 2012 at 22:50 | history | edited | David |
edited tags
|
|
| Feb 12, 2012 at 22:44 | comment | added | cardinal |
Is this homework (it kind of reads like it)? If so, please add the homework tag. For such questions, we will provide hints, but not full solutions, in general. It is helpful if you also edit the question to include the work you've done and what specifically you are finding challenging.
|
|
| Feb 12, 2012 at 22:43 | history | edited | cardinal | CC BY-SA 3.0 |
added 57 characters in body; edited title
|
| Feb 12, 2012 at 22:38 | history | asked | David | CC BY-SA 3.0 |