7.9 - Further Details on Exercise 7.9 = X(n) so that nxn1 n...

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Further Details on Exercise 7.9 ˆ θ = X ( n ) so that E ˆ θ = Z xf X ( n ) ( x ) dx = Z θ 0 x nx n - 1 θ n dx = n θ n Z θ 0 x n dx = n θ n θ n +1 n + 1 = n n + 1 θ E ˆ θ 2 = Z x 2 f X ( n ) ( x ) dx = Z θ 0 x 2 nx n - 1 θ n dx = n θ n Z θ 0 x n +1 dx = n θ n θ n +2 n + 2 = n n + 2 θ 2 Var( ˆ θ ) = n n + 2 θ 2 - ± n n + 1 θ ² 2 = 2 ( n + 2) ( n + 1) 2 . MSE = Bias 2 + Var = ± - θ n + 1 ² 2 + 2 ( n + 2) ( n + 1) 2 = 2 θ 2 ( n + 1) ( n + 2)
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This note was uploaded on 12/15/2011 for the course STAT 5326 taught by Professor Frade during the Fall '10 term at FSU.

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