I have multi-sample data which comprises distances between successive points on a line (1D vector), to which a gamma-distribution is fitted (and maximum likelihood parameters obtained). I would like to assess the quality of this fit.
I've read that GoF-tests such as the one-sample Kolmogorov-Smirnov (KS) or Anderson-Darling (AD) are inapplicable in this case and will produce inaccurate p-values because the theoretical distribution being compared to has been derived from the data itself and thus is not independent. Could anybody explain this further as i'm not sure I quite understand why it would be an issue?
Secondly, is bootstrap resampling (iterative sampling with replacement) a viable solution in this case to obtain more-accurate p-values and assessment of the fit? Following the resampling process and obtaining of, for example, KS-stats for each sample - how would one then "average" the results into a final conclusion/assessment or interpret the outcome?