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Unformatted text preview: 3. Adaptation of problems 2.82.12 in MN. Consider the following density, f x ( x ; , ) = (1x 2 ) 1 / 2 (12 x + 2 ) B ( + 1 / 2 , 1 / 2) ,1 x 1 . (1) for >1 / 2 and1 1 (note: B ( , ) is the beta function.) (a) Show that for xed , the density given above is in the exponential dispersion family. Identify the relevant components and identify the cumulant generating function. (b) Suppose X 1 , . . . , X n are iid with density given above. Derive the maximum likelihood estimate for for xed . Show that the mle is independent of by showing that the Fisher information matrix for ( , ) is diagonal. [Hint: feel free to use results from problems 2.82.11 in MN]...
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 Spring '08
 Daniels

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