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Suppose I wanted to know which of the skewness indexes 2 to 7 listed here is most precise in finite samples of fixed sizes drawn from a known skewed distribution.

How could I do this using simulations?

Just comparing their empirical variances won't do because they don't estimate skewness on the same scale. Normalizing the empirical variances by the mean skewness index (as is done in [0] for the case of dispersion measures) also won't do because the mean skewness could be very close to 0.

  • [0] P. J. Bickel and E. L. Lehmann. Descriptive Statistics for Nonparametric Models. III. Dispersion. Ann. Statist. Volume 4, Number 6 (1976), 1139-1158.
user603
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    What do you mean by 'precise' here? – Glen_b Dec 19 '14 at 09:58
  • @Glen_b: Im looking for an alternative to the normalized empirical variance which is used in [0] to measure finite sample efficiency because that concept (normalized empirical variance) does not work very well for estimates of skewness (for the reasons I explained in the question) – user603 Dec 19 '14 at 10:52

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