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.
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Received August 2000
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Uno, C., Isogai, E. Sequential point estimation of the powers of a normal scale parameter. Metrika 55, 215–232 (2002). https://doi.org/10.1007/s001840100143
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DOI: https://doi.org/10.1007/s001840100143