5 10 In Theorem 5 7, show that condition (i) allows the most shrinkage when 2I , for some value of 2 That is, show that for all r r positive definite , max tr max() tr 2I max(2I ) r Hint Write tr max() i max, where the is are the eigenvalues of ...

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5.10 In Theorem 5.7, show that condition (i) allows the most shrinkage when = 2I ,...

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5.10 In Theorem 5.7, show that condition (i) allows the most shrinkage when = σ2I , for some value of σ2. That is, show that for all r × r positive definite , max

λmax() = tr σ2I

λmax(σ2I ) = r.

[Hint: Write tr

λmax() = λi/λmax, where the λi’s are the eigenvalues of .]

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Theory Of Point Estimation

ISBN: 9780387985022

2nd Edition

Authors: Erich L. Lehmann, George Casella

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5.10 In Theorem 5.7, show that condition (i) allows the most shrinkage when = 2I ,...

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