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- W2000366397 abstract "In studying the variation of a variable subject to erratic trend effects, it is customary to employ as a measure of variation a statistic that eliminates most of such effects. It is shown in this paper that the statistic $w = sum^{n - 1}_1 |x_{i+1} - x_i| sqrt{pi}/2(n - 1)$ is nearly as efficient as the statistic $delta^2 = sum^{n - 1}_1 (x_{i+1} - x_i)^2/(n - 1)$ that is customarily employed. The asymptotic variance of w is obtained by integration techniques; the proof of the asymptotic normality of w is based upon a theorem of S. Bernstein on the asymptotic distribution of sums of dependent variables. The method of proof is sufficiently general to prove the asymptotic normality of w, and of $delta^2$, for $x$ having a distribution for which the third absolute moment exists." @default.
- W2000366397 created "2016-06-24" @default.
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- W2000366397 date "1946-12-01" @default.
- W2000366397 modified "2023-09-25" @default.
- W2000366397 title "The Efficiency of the Mean Moving Range" @default.
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- W2000366397 doi "https://doi.org/10.1214/aoms/1177730886" @default.
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