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Goodness-of-fit Criteria for the Adams and Jefferson Rounding Methods and their Limiting Laws

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Abstract

Multiplier methods are used to round probabilities on finitely many categories to rational proportions. Focusing on the classical methods of Adams and Jefferson, we investigate goodness-of-fit criteria for this rounding process. Assuming that the given probabilities are uniformly distributed, we derive the limiting laws of the criteria, first when the rounding accuracy increases, and then when the number of categories grows large.

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References

  • Aitchison J (1986) The statistical analysis of compositional data. Chapman and Hall, London

    MATH  Google Scholar 

  • Balinski ML, Young HP (2001) Fair representation – meeting the ideal of one man, one vote, 2nd edn. Brookings Institution Press, Washington

    Google Scholar 

  • Billingsley P (1999) Convergence of probability measures, 2nd edn. Wiley, New York

    MATH  Google Scholar 

  • Happacher M (2001) The discrepancy distribution of stationary multiplier rules for rounding probabilities. Metrika 53:171–181

    Article  MATH  MathSciNet  Google Scholar 

  • Heinrich L, Pukelsheim F, Schwingenschlögl U (2004) Sainte–Laguë’s chi-square divergence for the rounding of probabilities and its convergence to a stable law. Stat Decis 22:43–59

    Article  MATH  Google Scholar 

  • Heinrich L, Pukelsheim F, Schwingenschlögl U (2005) On stationary multiplier methods for the rounding of probabilities and the limiting law of the Sainte-Laguë divergence. Stat Decis 23:117–129

    Article  MATH  Google Scholar 

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Correspondence to Lothar Heinrich.

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Heinrich, L., Schwingenschlögl, U. Goodness-of-fit Criteria for the Adams and Jefferson Rounding Methods and their Limiting Laws. Metrika 64, 191–207 (2006). https://doi.org/10.1007/s00184-006-0044-0

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  • DOI: https://doi.org/10.1007/s00184-006-0044-0

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