IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v62y1997i1p137-168.html
   My bibliography  Save this article

Some New Statistics for Testing Hypotheses in Parametric Models,

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(97)91680-8
    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. L. Györfi & I. Vajda & E. Meulen, 1996. "Minimum kolmogorov distance estimates of parameters and parametrized distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 43(1), pages 237-255, December.
    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.
    3. 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.
    4. David Hinkley, 1974. "A Bibliography of Multivariate Statistical Analysis," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 23(3), pages 439-440, November.
    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. 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).
    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. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Chalabi, Yohan & Wuertz, Diethelm, 2012. "Portfolio optimization based on divergence measures," MPRA Paper 43332, University Library of Munich, Germany.
    11. 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.
    12. 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.
    13. B. Abraham & P. Sankaran, 2006. "Renyi's entropy for residual lifetime distribution," Statistical Papers, Springer, vol. 47(1), pages 17-29, January.
    14. 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.
    15. 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.

    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. Wegenkittl, Stefan, 2002. "A Generalized [phi]-Divergence for Asymptotically Multivariate Normal Models," Journal of Multivariate Analysis, Elsevier, vol. 83(2), pages 288-302, November.
    2. Tomáš Hobza & Domingo Morales & Leandro Pardo, 2014. "Divergence-based tests of homogeneity for spatial data," Statistical Papers, Springer, vol. 55(4), pages 1059-1077, November.
    3. Wang, P. C. & Lin, D. F., 2001. "Dispersion effects in signal-response data from fractional factorial experiments," Computational Statistics & Data Analysis, Elsevier, vol. 38(1), pages 95-111, November.
    4. 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.
    5. Abraão Nascimento & Jodavid Ferreira & Alisson Silva, 2023. "Divergence-based tests for the bivariate gamma distribution applied to polarimetric synthetic aperture radar," Statistical Papers, Springer, vol. 64(5), pages 1439-1463, October.
    6. Alba-Fernández, V. & Jiménez-Gamero, M.D., 2009. "Bootstrapping divergence statistics for testing homogeneity in multinomial populations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(12), pages 3375-3384.
    7. Conde, J. & Salicrú, M., 1998. "Uniform association in contingency tables associated to Csiszar divergence," Statistics & Probability Letters, Elsevier, vol. 37(2), pages 149-154, February.
    8. Valdevino Félix de Lima, Wenia & David Costa do Nascimento, Abraão & José Amorim do Amaral, Getúlio, 2021. "Distance-based tests for planar shape," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    9. 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.
    10. Stephen Satchell & Susan Thorp & Oliver Williams, 2012. "Estimating Consumption Plans for Recursive Utility by Maximum Entropy Methods," Research Paper Series 300, Quantitative Finance Research Centre, University of Technology, Sydney.
    11. Mora, Ricardo & Ruiz-Castillo, Javier, 2010. "A Kullback-Leibler measure of conditional segregation," UC3M Working papers. Economics we1015, Universidad Carlos III de Madrid. Departamento de Economía.
    12. Alejandro C. Frery & Juliana Gambini, 2020. "Comparing samples from the $${\mathcal {G}}^0$$G0 distribution using a geodesic distance," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(2), pages 359-378, June.
    13. Domingo Morales, 2019. "Comments on: Deville and Särndal’s calibration: revisiting a 25 years old successful optimization problem," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(4), pages 1068-1070, December.
    14. Menéndez, M. L. & Morales, D. & Pardo, L. & Zografos, K., 1999. "Statistical inference for finite Markov chains based on divergences," Statistics & Probability Letters, Elsevier, vol. 41(1), pages 9-17, January.
    15. Theobald, Chris M. & Talbot, Mike, 2004. "Bayesian selection of fertilizer level when crop price depends on quality," Computational Statistics & Data Analysis, Elsevier, vol. 47(4), pages 867-880, November.
    16. Kakizawa, Yoshihide, 1997. "Parameter estimation and hypothesis testing in stationary vector time series," Statistics & Probability Letters, Elsevier, vol. 33(3), pages 225-234, May.
    17. 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).
    18. Domingo Morales & Leandro Pardo, 2001. "Some approximations to power functions of ϕ-divergence tests in parametric models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 10(2), pages 249-269, December.
    19. Swanepoel, C. J. & Doku, W. O., 2003. "New goodness-of-fit tests for the error distribution of autoregressive time-series models," Computational Statistics & Data Analysis, Elsevier, vol. 43(3), pages 333-340, July.
    20. Alexander Katzur & Udo Kamps, 2020. "Classification using sequential order statistics," 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. 14(1), pages 201-230, March.

    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:62:y:1997:i:1:p:137-168. 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.