Sequential point estimation of the powers of a normal scale parameter |
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Authors: | Chikara Uno Eiichi Isogai |
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Institution: | (1) Department of Mathematics, Akita University, Akita 010-8502, Japan (e-mail: uno@math.akita-u.ac.jp), JP;(2) Department of Mathematics, Niigata University, Niigata 950-2181, Japan, JP |
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Abstract: | We consider the sequential point estimation problem of the powers of a normal scale parameter σr with r≠ 0 when the loss function is squared error plus linear cost. It is shown that the regret due to using our fully sequential
procedure in ignorance of σ is asymptotically minimized for estimating σ−2. We also propose a bias-corrected procedure to reduce the risk and show that the larger the distance between r and −2 is, the more effective our bias-corrected procedure is.
Received August 2000 |
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Keywords: | : Second order approximation fully sequential procedure regret uniform integrability bias-correction |
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