 My Math Forum Unbiased Estimator of the Standard Error of another Estimator

 February 8th, 2018, 06:48 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 $\tilde \theta=2\bar Y-1$. 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, 01:54 PM #2 Senior Member   Joined: Sep 2015 From: USA Posts: 2,468 Thanks: 1342 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 Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post calypso Advanced Statistics 5 January 7th, 2016 01:44 PM statssav Probability and Statistics 2 September 14th, 2015 01:33 PM nadroj Advanced Statistics 7 September 12th, 2014 12:59 AM PerMortenIvar Advanced Statistics 1 March 8th, 2012 12:14 PM mada2009 Advanced Statistics 0 January 29th, 2012 12:09 PM

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