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Some New Statistics for Testing Hypotheses in Parametric Models,


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  • Morales, D.
  • Pardo, L.
  • Vajda, I.
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    The paper deals with simple and composite hypotheses in statistical models with i.i.d. observations and with arbitrary families dominated by[sigma]-finite measures and parametrized by vector-valued variables. It introduces[phi]-divergence testing statistics as alternatives to the classical ones: the generalized likelihood ratio and the statistics of Wald and Rao. It is shown that, under the assumptions of standard type about hypotheses and model densities, the results about asymptotic distribution of the classical statistics established so far for the counting and Lebesgue dominating measures (discrete and continuous models) remain true also in the general case. Further, these results are extended to the[phi]-divergence statistics with smooth convex functions[phi]. The choice of[phi]-divergence statistics optimal from the point of view of power is discussed and illustrated by several examples.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 62 (1997)
    Issue (Month): 1 (July)
    Pages: 137-168

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    Handle: RePEc:eee:jmvana:v:62:y:1997:i:1:p:137-168

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    Keywords: parametric models simple and composite hypotheses asymptotic distributions of test statistics generalized likelihood ratio Wald's statistic Rao's statistic divergence statistics;


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    1. Salicru, M. & Morales, D. & Menendez, M. L. & Pardo, L., 1994. "On the Applications of Divergence Type Measures in Testing Statistical Hypotheses," Journal of Multivariate Analysis, Elsevier, vol. 51(2), pages 372-391, November.
    2. Menendez, M. & Morales, D. & Pardo, L. & Vajda, I., 1995. "Divergence-Based Estimation and Testing of Statistical Models of Classification," Journal of Multivariate Analysis, Elsevier, vol. 54(2), pages 329-354, August.
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    Cited by:
    1. B. Abraham & P. Sankaran, 2006. "Renyi's entropy for residual lifetime distribution," Statistical Papers, Springer, vol. 47(1), pages 17-29, January.
    2. Chalabi, Yohan & Wuertz, Diethelm, 2012. "Portfolio optimization based on divergence measures," MPRA Paper 43332, University Library of Munich, Germany.
    3. 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.
    4. Alessandro De Gregorio & Stefano Iacus, 2011. "On a family of test statistics for discretely observed diffusion processes," UNIMI - Research Papers in Economics, Business, and Statistics unimi-1114, Universit√° degli Studi di Milano.


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