  Power-law distributions have been widely observed in different areas of
scientific research. Practical estimation issues include how to select a
threshold above which observations follow a power-law distribution and then how
to estimate the power-law tail index. A minimum distance selection procedure
(MDSP) is proposed in Clauset et al. (2009) and has been widely adopted in
practice, especially in the analyses of social networks. However, theoretical
justifications for this selection procedure remain scant. In this paper, we
study the asymptotic behavior of the selected threshold and the corresponding
power-law index given by the MDSP. We find that the MDSP tends to choose too
high a threshold level and leads to Hill estimates with large variances and
root mean squared errors for simulated data with Pareto-like tails.
