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- W2003158614 abstract "Abstract This article examines the phenomenon of negative regret in sequential point estimation, in which a stopping rule used in ignorance of the variance of the distribution sometimes performs better than the best fixed sample size when the variance is known. An explanation in terms of a certain robustifying effect of the stopping rule is given. Results of simulation studies illustrating both negative regret and its explanation are also given. Suppose X 1 X 2, … are iid with mean μ and variance σ2. One may stop observing the sequence of X i′s after any number of observations n and estimate μ by the sample mean , subject to the loss . If σ is known, then the best fixed (i.e., nonrandom) sample size, in the sense of minimum risk, can be used. If σ is unknown, the best fixed sample size is unknown, necessitating a sequential procedure. For a sequential procedure of the type first proposed by Robbins (1959), the “regret”—expected additional loss from not knowing σ and using the sequential procedure instead of the best fixed sample size—can take arbitrarily large negative values. This is explained by noting that the sequential procedure acts to control extreme values and can be viewed as a sequential analog of trimming and Winsorizing in the nonsequential setting. I illustrate analytically by showing that the sequential procedure reduces the mean squared error of the sample mean when the distribution of the X i′s is symmetric about μ and has large kurtosis. Simulation results show that both negative regret and its explanation can occur when the expected sample size is as small as 25 or 30." @default.
- W2003158614 created "2016-06-24" @default.
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- W2003158614 date "1988-03-01" @default.
- W2003158614 modified "2023-09-24" @default.
- W2003158614 title "Negative Regret, Optional Stopping, and the Elimination of Outliers" @default.
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- W2003158614 doi "https://doi.org/10.1080/01621459.1988.10478581" @default.
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