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Sequential point estimation of the powers of a normal scale parameter
Authors:Chikara Uno  Eiichi Isogai
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
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
Keywords:: Second order approximation  fully sequential procedure  regret  uniform integrability  bias-correction
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