I would like to systematically study the slopes of power-law frequency spectra, having multiple scaling ranges, but I cannot find any detailed analysis of the problem. I am not happy with least-square fitting log-log transformed data as it can easily give very biased results. I found something on fitting power-law binned data in the paper I link, but I was hoping for a much more specific investigation.

To cut it short: I would like to find a statistical discussion of the fit of power-law spectra to

Thanks!

http://projecteuclid.org/euclid.aoas/1396966280