Fisher information

Asked Mar 21 '13 at 10:42

Active Aug 10 '13 at 08:16

Viewed 127 times

Hello how to show the following:

Observations $(X_1,X_2,..,X_n,)$ are i.i.d. over $[0,2\pi)$ with density $f(x,\theta) = \exp[\theta_1\cos x + \theta_2 \sin x -c(\theta)]$ where $\theta =(\theta_1,\theta_2) \in R^2$

Find an expression for the Fisher information $I(\theta)$ involving integrals and show that it is positive definite for all $\theta \in R^2$

Thank you!

edited Aug 10 '13 at 08:16

Nick Cox

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asked Mar 21 '13 at 10:42

Salih Ucan

Do you know the definition of $I(\theta)$? – Zen Mar 22 '13 at 20:30
Yes @Zen i do but how to show the positive definiteness? – Salih Ucan Mar 23 '13 at 10:18
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It is proved here: http://stats.stackexchange.com/questions/49942/why-is-the-fisher-information-matrix-positive-semidefinite/49961#49961 – Zen Mar 23 '13 at 12:31

Fisher information

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