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An estimation method for the Neyman chi-square divergence with application to test of hypotheses

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  • Broniatowski, M.
  • Leorato, S.

Abstract

We propose a new definition of the Neyman chi-square divergence between distributions. Based on convexity properties and duality, this version of the [chi]2 is well suited both for the classical applications of the [chi]2 for the analysis of contingency tables and for the statistical tests in parametric models, for which it is advocated to be robust against outliers. We present two applications in testing. In the first one, we deal with goodness-of-fit tests for finite and infinite numbers of linear constraints; in the second one, we apply [chi]2-methodology to parametric testing against contamination.

Suggested Citation

  • Broniatowski, M. & Leorato, S., 2006. "An estimation method for the Neyman chi-square divergence with application to test of hypotheses," Journal of Multivariate Analysis, Elsevier, vol. 97(6), pages 1409-1436, July.
    • Handle: RePEc:eee:jmvana:v:97:y:2006:i:6:p:1409-1436
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    References listed on IDEAS

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    1. Morales, D. & Pardo, L. & Vajda, I., 1997. "Some New Statistics for Testing Hypotheses in Parametric Models, ," Journal of Multivariate Analysis, Elsevier, vol. 62(1), pages 137-168, July.
    2. Raúl Jiménz & Yongzhao Shao, 2001. "On robustness and efficiency of minimum divergence estimators," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 10(2), pages 241-248, December.
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    Cited by:

    1. Toma, Aida & Broniatowski, Michel, 2011. "Dual divergence estimators and tests: Robustness results," Journal of Multivariate Analysis, Elsevier, vol. 102(1), pages 20-36, January.
    2. Broniatowski, Michel, 2014. "Minimum divergence estimators, maximum likelihood and exponential families," Statistics & Probability Letters, Elsevier, vol. 93(C), pages 27-33.
    3. Cerqueti, Roy & Maggi, Mario, 2021. "Data validity and statistical conformity with Benford’s Law," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).

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