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Some New Statistics for Testing Hypotheses in Parametric Models,

Author

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  • Morales, D.
  • Pardo, L.
  • Vajda, I.

Abstract

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.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:jmvana:v:62:y:1997:i:1:p:137-168
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    References listed on IDEAS

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    1. 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.
    2. 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.
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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. 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.
    3. De Gregorio, A. & Iacus, S.M., 2013. "On a family of test statistics for discretely observed diffusion processes," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 292-316.
    4. Chalabi, Yohan & Wuertz, Diethelm, 2012. "Portfolio optimization based on divergence measures," MPRA Paper 43332, University Library of Munich, Germany.
    5. Alessandro De Gregorio & Stefano Iacus, 2009. "Pseudo phi-divergence test statistics and multidimensional Ito processes," UNIMI - Research Papers in Economics, Business, and Statistics unimi-1083, Universitá degli Studi di Milano.

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