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Unformatted text preview: L ( X 1 ,X 2 ,...,X n  ) denote the likelihood function of the data under parameter value , set: n = sup R L ( X 1 ,X 2 ,...,X n  ) L ( X 1 ,X 2 ,...,X n  ) . Show that when is the true value of generating the data, 2 log n converges to a 2 1 distribution, using Taylor expansions. (v) Let K ( , 1 ) = E [log ( p ( X 1 , ) /p ( X 1 , 1 ))] denote the KulbackLeibler distance between and 1 . Show that this is nonnegative. If 1 6 = is the true value of generating the data, show that 2 log n /n converges in probability to K ( , 1 ). 1...
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 Fall '09
 moulib

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