Sequential point estimation of the powers of a normal scale parameter

被引：0
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作者：
Chikara Uno
Eiichi Isogai
机构：
[1] Department of Mathematics,
[2] Akita University,undefined
[3] Akita 010-8502,undefined
[4] Japan (e-mail: uno@math.akita-u.ac.jp),undefined
[5] Department of Mathematics,undefined
[6] Niigata University,undefined
[7] Niigata 950-2181,undefined
[8] Japan,undefined
来源：
Metrika | 2002年 / 55卷
关键词：
Key words: Second order approximation; fully sequential procedure; regret; uniform integrability; bias-correction;
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摘要：
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.
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页码：215 / 232
页数：17
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