Tagged Questions

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Question on expected value of an estimator

I have been given the pdf: $$f_{\theta}(x)=\frac{x}{\theta^2}e^{-\frac{x^2}{2\theta^2}}$$ and I want to know if the MLE estimator $\theta$ is unbiased. Attempt: I want to maximize the function so I ...
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Is it possible to have an estimator that is unbiased and bounded?

I have a parameter $\theta$ which lies between $[0,1]$. Let us say that I can run an experiment and obtain $\hat{\theta} = \theta + w$, where $w$ is a standard Gaussian. What I need is an estimate of ...
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Unbiased hypothesis tests

Is there some textbook or expository account showing that the definition of "unbiased test" bears the same sort of relation to "unbiased estimator" that interval estimation generally bears to ...
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counterexample for the sufficient condition required for consistency

We know that if an estimator is an unbiased estimator of theta and if its variance tends to 0 as n tends to infinity then it is a consistent estimator for theta. But this is a sufficient and not a ...
Let $X_1, \dots, X_n$ denote a random sample of size n from the probability distribution with pdf: $$f_X(x|\theta_1, \theta_2) = \frac{1}{\theta_2 - \theta_1} \ I(x)_{[\theta_1,\theta_2]} \ ... 1answer 219 views What is the UMVUE for \sigma^2 in \mathcal N(0, \sigma^2 )? By using the exponential class factorization theorem, I came up with Y = \sum (x_i)^2 to be the complete and sufficient statistics for \sigma^2 . Using this sufficient statistic as a condition, ... 1answer 395 views Does efficiency imply unbiased and consistency? If I can prove that for an estimator \hat{k}( \theta) I can write:$$\frac{\partial l(X_1, \dots , X_n)}{\partial \theta} = a(n, \theta)(\hat{\theta} - \theta) Am i sure that the estimator is ...
$X_1, X_2, \ldots, X_n$ is a random sample from $\mathrm{Bernoulli}(\theta)$, $\epsilon_1, \epsilon_2, \ldots, \epsilon_n$ are independent $\mathcal N(0, \sigma^2)$, independent of $X_i$. Define ...