Goodness-of-fit criteria for the Adams and Jefferson rounding methods and their limiting laws
Let \(W = (w_1, \dots, w_c)\) be some arbitrary probability vector for a fixed number of categories \(c\). The arbitrariness is modelled by assuming \(W\) to be random and, moreover, to follow a continuous distribution on the probability simplex \[ S_c = \{(w_1, \dots, w_c) \in [0, 1]^c : w_1 + \dots + w_c = 1\}. \] Rounding methods are used to round the continuous weights \(W_i\) to rational proportions of the form \(N_i/n\) for some prescribed integer accuracy \(n\). Implementing the classical methods of Adams and Jefferson, the authors investigate goodness-of-fit criteria for this rounding process. Assuming that the given probabilities are uniformly distributed, the limiting laws of the criteria are derived, first when the rounding accuracy increases, and then when the number of categories grows large.
scientific article; zbMATH DE number 5073833