Bock (1975, TheoremA) established that for X N(, I K ) then for any scalar function g (x) E Xh X0X E h (QK2) where QK2 2 K2() Assume b N(, I K ) and eJS 1 K 2 b0b b (a) Use Bocks result to calculate E 1 b0b b You can represent your answer using the function JK (b) Calculate the bias of eJS (c) Desc...

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Bock (1975, TheoremA) established that for X N(, I K ) then for any scalar function

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Bock (1975, TheoremA) established that for X » N(µ, I K ) then for any scalar function g (x)

X0X

¢¤

Æ µE[h (QKÅ2)]

where QKÅ2 » Â2 KÅ2(¸). Assume bµ » N(µ, I K ) and eµJS Æ

1¡

K ¡2 bµ0bµ

bµ.

(a) Use Bock’s result to calculate E

1 bµ0bµ

bµ

. You can represent your answer using the function JK .

(b) Calculate the bias of eµJS.

(c) Describe the bias. Is the estimator biased downwards, upwards, or towards zero?

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Probability And Statistics For Economists

ISBN: 9780691235943

1st Edition

Authors: Bruce Hansen

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Question Posted: Sep 23, 2024 07:01 AM

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Bock (1975, TheoremA) established that for X N(, I K ) then for any scalar function

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Probability And Statistics For Economists

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