
Advanced Statistics Advanced Probability and Statistics Math Forum 
 LinkBack  Thread Tools  Display Modes 
February 8th, 2018, 07:48 PM  #1 
Senior Member Joined: Oct 2015 From: Antarctica Posts: 128 Thanks: 0  Unbiased Estimator of the Standard Error of another Estimator
Suppose that $Y_1,...,Y_n$ is an IID sample from a uniform $U(\theta, 1)$ distribution. The method of moments estimator for $\theta$ is $\tilde \theta=2\bar Y1$. The standard error of $\tilde \theta$ is $$\sigma_{\tilde \theta}=\frac{1\theta}{\sqrt{3n}}$$ Find an unbiased estimator of $\sigma_{\tilde \theta}$ and show that it is unbiased. So normally I know how to find the estimator of a parameter of a distribution, but I don't quite understand how I'm supposed to find an estimator of the standard deviation of another estimator of a parameter of a distribution... so I really don't know how to go about this. What do I do? 
February 9th, 2018, 02:54 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,203 Thanks: 1157 
this turned out to be so simple that I'm just embarrassed about the effort it took. $\begin{align*} &\sigma_{\tilde{\theta}} \approx \dfrac{1  (2\overline{Y}1)}{\sqrt{3n}} =\\ \\ &\dfrac{2(1\overline{Y})}{\sqrt{3n}} ; \\ \\ &E[\sigma_{\tilde{\theta}}] = \dfrac{2\left(1\frac{1+\theta}{2}\right)}{\sqrt{3n}} = \\ \\ &\dfrac{1\theta}{\sqrt{3n}} \end{align*}$ 

Tags 
error, estimator, standard, unbiased 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Estimator for mean  calypso  Advanced Statistics  5  January 7th, 2016 02:44 PM 
Shortcut Formula for the Unbiased Estimator  statssav  Probability and Statistics  2  September 14th, 2015 02:33 PM 
Unbiased estimator proof  nadroj  Advanced Statistics  7  September 12th, 2014 01:59 AM 
bias estimator  PerMortenIvar  Advanced Statistics  1  March 8th, 2012 01:14 PM 
Unbiased Estimator  Order Statistic  mada2009  Advanced Statistics  0  January 29th, 2012 01:09 PM 