Goodness-of-fit criteria for the Adams and Jefferson rounding methods and their limiting laws
type: Item
instance of: scholarly article
title: Goodness-of-fit criteria for the Adams and Jefferson rounding methods and their limiting laws
zbMATH Open document ID: 1125.65040
author: U. Schwingenschlögl
author: Lothar Heinrich
published in: Metrika
publication date: 2006-11-17T00:00:00Z
review text: 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.
reviewed by: Petko Hr. Petkov
Mathematics Subject Classification ID: 65G50
zbMATH DE Number: 5073833
zbMATH Keywords: appointment method
zbMATH Keywords: rounding error analysis
zbMATH Keywords: Gaussian limit law
zbMATH Keywords: q-stationary multiplier method
zbMATH Keywords: Sainte-Laguë divergence
zbMATH Keywords: convergence in distribution
zbMATH Keywords: goodness-of-fit criteria
MaRDI profile type: Publication
full work available at URL: s00184-006-0044-0
OpenAlex ID: W2063432805
cites work: Q4207468
cites work: Q4269108
cites work: The discrepancy distribution of stationary multiplier rules for rounding probabilities
cites work: Sainte-Laguë’s chi-square divergence for the rounding of probabilities and its convergence to a stable law
cites work: On stationary multiplier methods for the rounding of probabilities and the limiting law of the Sainte-Laguë divergence
DOI: 10.1007/S00184-006-0044-0
description: scientific article; zbMATH DE number 5073833