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Asymptotic distributions for goodness-of-fit statistics in a sequence of multinomial models

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  • Györfi, L.
  • Vajda, I.

Abstract

We consider f-disparities between discrete distributions pn=(pn1,...,pnkn) and their estimates based on relative frequencies in an i.i.d. sample of size n, where is twice continuously differentiable in a neighborhood of 1 with f''(1)[not equal to]0. We derive asymptotic distributions of the disparity statistics under certain assumptions about pn and the second derivatives f'' in a neighborhood of 1. These assumptions are weaker than those known from the literature.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:56:y:2002:i:1:p:57-67
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    References listed on IDEAS

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    1. 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.
    2. Györfi László & Vajda Igor, 2001. "A Class Of Modified Pearson And Neyman Statistics," Statistics & Risk Modeling, De Gruyter, vol. 19(3), pages 239-252, March.
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    Cited by:

    1. 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.

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