Tagged Questions

3
votes
0answers
89 views

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 ...
0
votes
0answers
31 views

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 ...
3
votes
2answers
131 views

Sufficient statistics, MLE and unbiased estimators of uniform type distribution

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]} \ ...
5
votes
1answer
175 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, ...
1
vote
1answer
280 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 ...
2
votes
1answer
347 views

How to show unbiased estimator of combination of bernoulli and normal variables?

$X_1, X_2, \ldots, X_n$ 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 ...