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Asymptotic distributions of φ‐divergences of hypothetical and observed frequencies on refined partitions

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  • M. L. Menéndez
  • D. Morales
  • L. Pardo
  • I. Vajda

Abstract

For a wide class of goodness‐of‐fit statistics based on φ‐divergences between hypothetical cell probabilities and observed relative frequencies, the asymptotic normality is established under the assumption n/mn→γ∈(0,∞), where n denotes sample size and mn the number of cells. Related problems of asymptotic distributions of φ‐divergence errors, and of φ‐divergence deviations of histogram estimators from their expected values, are considered too.

Suggested Citation

  • M. L. Menéndez & D. Morales & L. Pardo & I. Vajda, 1998. "Asymptotic distributions of φ‐divergences of hypothetical and observed frequencies on refined partitions," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 52(1), pages 71-89, March.
    • Handle: RePEc:bla:stanee:v:52:y:1998:i:1:p:71-89
    DOI: 10.1111/1467-9574.00069
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    Cited by:

    1. Györfi, L. & Vajda, I., 2002. "Asymptotic distributions for goodness-of-fit statistics in a sequence of multinomial models," Statistics & Probability Letters, Elsevier, vol. 56(1), pages 57-67, January.
    2. Broniatowski, Michel & Keziou, Amor, 2009. "Parametric estimation and tests through divergences and the duality technique," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 16-36, January.
    3. Rempała, Grzegorz A. & Wesołowski, Jacek, 2016. "Double asymptotics for the chi-square statistic," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 317-325.
    4. Morales, D. & Pardo, L. & Vajda, I., 2003. "Asymptotic laws for disparity statistics in product multinomial models," Journal of Multivariate Analysis, Elsevier, vol. 85(2), pages 335-360, May.

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