a1 Purdue University
We study the finite-sample bias and mean squared error, when properly defined, of the sample coefficient of variation under a general distribution. We employ a Nagar-type expansion and use moments of quadratic forms to derive the results. We find that the approximate bias depends on not only the skewness but also the kurtosis of the distribution, whereas the approximate mean squared error depends on the cumulants up to order 6.
The author is grateful to the co-editor Paolo Paruolo and two anonymous referees for helpful comments. The author is solely responsible for any remaining errors.