Goodness-of-fit statistics for location-scale distributions

Goodness-of-Fit Statistics for Discrete Multivariate Data

“…When the number of cells is chosen to be of the same order of magnitude as the sample size. Gan (1985) derives the asymptotic distribution of X 2 to be normal provided 0 is a one-dimensional location parameter estimated by the ungrouped sample median (Sections 4.3 and 8.1).…”

“…However Koehler notes that bias of the estimated moments is a potential problem for very sparse tables, and that the speed of convergence to the asymptotic distribution appears slow. For testing the goodness of fit of a continuous parametric distribution function with unknown location parameter, Gan (1985) shows that X 2 (A. = 1) is asymptotically normal when the (location) parameter is estimated via the ungrouped sample median.…”

“…When the number of cells increases with n, Gan (1985) derives the asymptotic normality of X 2 when 0 is a one-dimensional location parameter estimated via the ungrouped sample median. This result parallels those under the sparseness assumptions in Section 4.3 (Section 8.1).…”