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.