IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v97y2006i6p1409-1436.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(06)00019-4
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. Ayman Hijazy & András Zempléni, 2021. "Gamma Process-Based Models for Disease Progression," Methodology and Computing in Applied Probability, Springer, vol. 23(1), pages 241-255, March.
    4. Alessandro DE GREGORIO & Stefano Maria IACUS, 2011. "On a family of test statistics for discretely observed diffusion processes," Departmental Working Papers 2011-37, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    5. Leorato, S., 2009. "A refined Jensen's inequality in Hilbert spaces and empirical approximations," Journal of Multivariate Analysis, Elsevier, vol. 100(5), pages 1044-1060, May.
    6. Nada M. Alfaer & Ahmed M. Gemeay & Hassan M. Aljohani & Ahmed Z. Afify, 2021. "The Extended Log-Logistic Distribution: Inference and Actuarial Applications," Mathematics, MDPI, vol. 9(12), pages 1-22, June.
    7. Martín, Nirian & Balakrishnan, Narayanaswami, 2011. "Hypothesis testing in a generic nesting framework with general population distributions," DES - Working Papers. Statistics and Econometrics. WS ws113527, Universidad Carlos III de Madrid. Departamento de Estadística.
    8. Diaa Al Mohamad, 2018. "Towards a better understanding of the dual representation of phi divergences," Statistical Papers, Springer, vol. 59(3), pages 1205-1253, September.
    9. N. Martín & L. Pardo & K. Zografos, 2019. "On divergence tests for composite hypotheses under composite likelihood," Statistical Papers, Springer, vol. 60(6), pages 1883-1919, December.
    10. Alessandro DE GREGORIO & Stefano Maria IACUS, 2009. "Pseudo phi-divergence test statistics and multidimensional Ito processes," Departmental Working Papers 2009-48, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    11. Basu, Ayanendranath & Chakraborty, Soumya & Ghosh, Abhik & Pardo, Leandro, 2022. "Robust density power divergence based tests in multivariate analysis: A comparative overview of different approaches," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    12. Ahmed Z. Afify & Ahmed M. Gemeay & Noor Akma Ibrahim, 2020. "The Heavy-Tailed Exponential Distribution: Risk Measures, Estimation, and Application to Actuarial Data," Mathematics, MDPI, vol. 8(8), pages 1-28, August.
    13. A. Gregorio & S. M. Iacus, 2019. "Empirical $$L^2$$ L 2 -distance test statistics for ergodic diffusions," Statistical Inference for Stochastic Processes, Springer, vol. 22(2), pages 233-261, July.
    14. Jiménez-Gamero, M.D. & Pino-Mejías, R. & Alba-Fernández, V. & Moreno-Rebollo, J.L., 2011. "Minimum [phi]-divergence estimation in misspecified multinomial models," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3365-3378, December.
    15. 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.
    16. Toma, Aida & Broniatowski, Michel, 2011. "Dual divergence estimators and tests: Robustness results," Journal of Multivariate Analysis, Elsevier, vol. 102(1), pages 20-36, January.
    17. Chalabi, Yohan & Wuertz, Diethelm, 2012. "Portfolio optimization based on divergence measures," MPRA Paper 43332, University Library of Munich, Germany.
    18. B. Abraham & P. Sankaran, 2006. "Renyi's entropy for residual lifetime distribution," Statistical Papers, Springer, vol. 47(1), pages 17-29, January.
    19. J. A. Pardo & M. C. Pardo, 2008. "Minimum Φ-Divergence Estimator and Φ-Divergence Statistics in Generalized Linear Models with Binary Data," Methodology and Computing in Applied Probability, Springer, vol. 10(3), pages 357-379, September.
    20. Elena Castilla & Abhik Ghosh & Nirian Martin & Leandro Pardo, 2021. "Robust semiparametric inference for polytomous logistic regression with complex survey design," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 15(3), pages 701-734, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:97:y:2006:i:6:p:1409-1436. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.