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Hypothesis testing in a generic nesting framework for general distributions

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  • Martín, N.
  • Balakrishnan, N.

Abstract

Nested parameter spaces, either in the null or alternative hypothesis, often enable an improvement in the performance of the tests. In this context, order restricted inference has not been studied in detail. Divergence based measures provide a flexible tool for proposing some useful test statistics, which usually contain the likelihood ratio-test statistics as a special case. The existing literature on hypothesis testing under inequality constraints, based on phi-divergence measures, is concentrated on specific models with multinomial sampling. In this paper the existing results are extended and unified through new families of test-statistics that are valid for nested parameter spaces containing either equality or inequality constraints and general distributions for either single or multiple populations.

Suggested Citation

  • Martín, N. & Balakrishnan, N., 2013. "Hypothesis testing in a generic nesting framework for general distributions," Journal of Multivariate Analysis, Elsevier, vol. 118(C), pages 1-23.
    • Handle: RePEc:eee:jmvana:v:118:y:2013:i:c:p:1-23
    DOI: 10.1016/j.jmva.2013.03.012
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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.
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    3. M.L. Menéndez & J.A. Pardo & L. Pardo, 2003. "Theory & Methods: Tests for Bivariate Symmetry Against Ordered Alternatives in Square Contingency Tables," Australian & New Zealand Journal of Statistics, Australian Statistical Publishing Association Inc., vol. 45(1), pages 115-123, March.
    4. K. Zografos, 1998. "f-Dissimilarity of Several Distributions in Testing Statistical Hypotheses," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(2), pages 295-310, June.
    5. 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. Martin, Nirian & Mata, Raquel & Pardo, Leandro, 2016. "Wald type and phi-divergence based test-statistics for isotonic binomial proportions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 120(C), pages 31-49.
    2. Martin, Nirian & Mata, Raquel & Pardo, Leandro, 2014. "Phi-divergence statistics for the likelihood ratio order: An approach based on log-linear models," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 387-408.
    3. A. Basu & A. Mandal & N. Martin & L. Pardo, 2018. "Testing Composite Hypothesis Based on the Density Power Divergence," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(2), pages 222-262, November.

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