List questions from statistical-inference

Published on 22 Mar 2026 - 15:30

129

Views

Understanding the density function and expected value of an estimator.

Published on 24 Mar 2026 - 23:43

216

Views

About L2 error distribution and its STRANGE oscillatory behaviour

Published on 20 Mar 2026 - 12:14

615

Views

Derive a sufficient statistic for $\theta$.

Published on 17 Mar 2026 - 6:21

50

Views

Rejecting null based on the likelihood ratio test

Published on 22 Mar 2026 - 10:13

480

Views

Uniformly minimum variance unbiased estimator of theta.

Published on 22 Mar 2026 - 15:35

90

Views

Show that the posterior probability of $H_0$ equals $\Phi\left(\sqrt{n}\frac{\theta_o -\bar{X}_n}{\sigma}\right)$

Published on 13 Mar 2026 - 8:38

215

Views

Derive an expression for the $p$-value using a test with test statistic $T =\sqrt{n}(\bar{X}_n - \theta_0)/\sigma$

Published on 12 Mar 2026 - 22:47

102

Views

Derive the posterior density of $\Theta$.

Published on 17 Mar 2026 - 4:38

152

Views

Transformation of MVN random variable

Published on 21 Mar 2026 - 22:08

211

Views

Show that $\hat{\theta}$ is not minimax.

Published on 22 Mar 2026 - 7:19

50

Views

Order statistics, unclear derivation of the distribution function, uniform df

Published on 22 Mar 2026 - 21:03

258

Views

Show that $T(X) = \min(X_1,\ldots,X_n)$ is a sufficient statistic using the factorisation theorem.

Published on 22 Mar 2026 - 4:42

1.1k

Views

Expected Value for a combination of IID from $f(x,\theta) = \frac{ \theta }{x^{ \theta + 1}}$

Published on 22 Mar 2026 - 14:58

247

Views

Variance of $T_n = \min_i \{ X_i \} + \max_i \{ X_i \}$

Published on 17 Mar 2026 - 15:50

List Question

Show that $d_2$ is the Bayes rule if the posterior mean of $\theta$ is greater than $1/2$.

Understanding the density function and expected value of an estimator.

About L2 error distribution and its STRANGE oscillatory behaviour

Derive a sufficient statistic for $\theta$.

Rejecting null based on the likelihood ratio test

Uniformly minimum variance unbiased estimator of theta.

Show that the posterior probability of $H_0$ equals $\Phi\left(\sqrt{n}\frac{\theta_o -\bar{X}_n}{\sigma}\right)$

Derive an expression for the $p$-value using a test with test statistic $T =\sqrt{n}(\bar{X}_n - \theta_0)/\sigma$

Derive the posterior density of $\Theta$.

Transformation of MVN random variable

Show that $\hat{\theta}$ is not minimax.

Order statistics, unclear derivation of the distribution function, uniform df

Show that $T(X) = \min(X_1,\ldots,X_n)$ is a sufficient statistic using the factorisation theorem.

Expected Value for a combination of IID from $f(x,\theta) = \frac{ \theta }{x^{ \theta + 1}}$

Variance of $T_n = \min_i \{ X_i \} + \max_i \{ X_i \}$

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