I'm looking at some data that conform reasonably well to a continuous power law distribution, according to a Kolmogorov-Smirnov test that compares the estimated power-law fit to the data (per Clauset, Shalizi, and Newman (2009), "Power-law distributions in empirical data," SIAM Review). The problem I'm facing is that I'm not exactly sure what current best practice is for looking for change points for the slope coefficient of that distribution.
Most change-point algorithms, as I understand it, aren't designed to work with long-tailed distributions, in which sample means converge only very slowly to population means. I can't estimate slope coefficients via OLS and then compare the coefficient on one side of the proposed change point vs. the coefficient on the other because the ranking procedure produces serial correlation among residuals, which means that the standard errors can be grossly understated (Gabaix and Ioannides (2004), "The Evolution of City Size Distributions," in Henderson and Thisse, Handbook of Regional and Urban Economics, volume 4). And the Hill MLE estimator is troublesome in finite samples (in the smallest sample, I'm looking at an n of under 100).
I could perhaps (?) bootstrap the coefficients to get the standard errors right or put together a likelihood ratio test, but I'm starting to wonder whether I'm making the problem bigger than it is. Couldn't I just use a two-sample Kolmogorov-Smirnov test to calculate the probability that the distributions on either side of the proposed change point differ? That strikes me as fairly intuitive and reasonably safe, but I'm coming to the realization that long-tailed distributions are the graveyard of statistical procedures that seem intuitive and safe. Since the empirics of power-law distributions seems to be an area of active development, I thought it would be best to consult the hive mind. Thanks in advance.