IDEAS home Printed from https://ideas.repec.org/p/vic/vicewp/0404.html
   My bibliography  Save this paper

The Behrens-Fisher Problem: An Empirical Likelihood Ratio Approach

Author

Listed:
  • Lauren Bin Dong

    (Statistics Canada)

Abstract

A new theoretical solution to the Behrens-Fisher (BF) problem is developed using empirical likelihood method. The sampling properties of the empirical likelihood ratio (ELR) test for the BF problem are derived using Monte Carlo simulation technique for a wide range of situations. A comparison of the size and power of the ELR test and the Welch-Aspin test is conducted for a special case of small sample sizes. The empirical results indicate that the ELR test for the BF problem has good power properties.

Suggested Citation

  • Lauren Bin Dong, 2004. "The Behrens-Fisher Problem: An Empirical Likelihood Ratio Approach," Econometrics Working Papers 0404, Department of Economics, University of Victoria.
    • Handle: RePEc:vic:vicewp:0404
    Note: ISSN 1485-6441
    as

    Download full text from publisher

    File URL: https://www.uvic.ca/socialsciences/economics/_assets/docs/econometrics/ewp0404.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. repec:cup:cbooks:9780521623940 is not listed on IDEAS
    2. Lauren Bin Dong & David E. A. Giles, 2004. "An Empirical Likelihood Ratio Test for Normality," Econometrics Working Papers 0401, Department of Economics, University of Victoria.
    3. Giles, Judith A & Giles, David E A, 1993. "Pre-test Estimation and Testing in Econometrics: Recent Developments," Journal of Economic Surveys, Wiley Blackwell, vol. 7(2), pages 145-197, June.
    4. Jing, Bing-Yi, 1995. "Two-sample empirical likelihood method," Statistics & Probability Letters, Elsevier, vol. 24(4), pages 315-319, September.
    5. Mittelhammer, Ronald C. & Judge, George G. & Schoenberg, Ron, 2003. "Empirical Evidence Concerning the Finite Sample Performance of EL-Type Structural Equation Estimation and Inference Methods," CUDARE Working Papers 25090, University of California, Berkeley, Department of Agricultural and Resource Economics.
    6. Bera, Anil K. & Bilias, Yannis, 2002. "The MM, ME, ML, EL, EF and GMM approaches to estimation: a synthesis," Journal of Econometrics, Elsevier, vol. 107(1-2), pages 51-86, March.
    7. Weerahandi, Samaradasa, 1987. "Testing Regression Equality with Unequal Variances," Econometrica, Econometric Society, vol. 55(5), pages 1211-1215, September.
    Full references (including those not matched with items on IDEAS)

    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. Lauren Bin Dong & David E. A. Giles, 2004. "An Empirical Likelihood Ratio Test for Normality," Econometrics Working Papers 0401, Department of Economics, University of Victoria.
    2. Giuseppe Ragusa, 2011. "Minimum Divergence, Generalized Empirical Likelihoods, and Higher Order Expansions," Econometric Reviews, Taylor & Francis Journals, vol. 30(4), pages 406-456, August.
    3. Umut Oguzoglu & Thanasis Stengos, 2011. "Can Dynamic Panel Data Explain the Finance-Growth Link? An Empirical Likelihood Approach," Review of Economic Analysis, Digital Initiatives at the University of Waterloo Library, vol. 3(2), pages 129-148, October.
    4. Judge, George G. & Mittelhammer, Ronald C., 2004. "Estimating the Link Function in Multinomial Response Models under Endogeneity and Quadratic Loss," CUDARE Working Papers 25095, University of California, Berkeley, Department of Agricultural and Resource Economics.
    5. Marian Grendar & George Judge, 2008. "Large-Deviations Theory and Empirical Estimator Choice," Econometric Reviews, Taylor & Francis Journals, vol. 27(4-6), pages 513-525.
    6. Lauren Bin Dong, 2004. "Testing for structural Change in Regression: An Empirical Likelihood Ratio Approach," Econometrics Working Papers 0405, Department of Economics, University of Victoria.
    7. Patrik Guggenberger, 2006. "Finite-Sample Evidence Suggesting a Heavy Tail Problem of the Generalized Empirical Likelihood Estimator, accepted for publication, Econometric Reviews," UCLA Economics Online Papers 371, UCLA Department of Economics.
    8. Miller, Douglas J. & Mittelhammer, Ronald C. & Judge, George G., 2004. "Entropy-Based Estimation And Inference In Binary Response Models Under Endogeneity," 2004 Annual meeting, August 1-4, Denver, CO 20319, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    9. MacKinnon, J G, 1989. "Heteroskedasticity-Robust Tests for Structural Change," Empirical Economics, Springer, vol. 14(2), pages 77-92.
    10. Clarke, Judith A., 2008. "On weighted estimation in linear regression in the presence of parameter uncertainty," Economics Letters, Elsevier, vol. 100(1), pages 1-3, July.
    11. Badi H. Baltagi & Peter Egger & Michael Pfaffermayr, 2007. "A Monte Carlo Study for Pure and Pretest Estimators of a Panel Data Model with Spatially Autocorrelated Disturbances," Annals of Economics and Statistics, GENES, issue 87-88, pages 11-38.
    12. Timothy K.M. Beatty, 2007. "Recovering the Shadow Value of Nutrients," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 89(1), pages 52-62.
    13. Taylor Sandra & Pollard Katherine, 2009. "Hypothesis Tests for Point-Mass Mixture Data with Application to `Omics Data with Many Zero Values," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 8(1), pages 1-45, February.
    14. T. W. Anderson & Naoto Kunitomo & Yukitoshi Matsushita, 2008. "On Finite Sample Properties of Alternative Estimators of Coefficients in a Structural Equation with Many Instruments," CIRJE F-Series CIRJE-F-577, CIRJE, Faculty of Economics, University of Tokyo.
    15. Robert Drake & Apratim Guha, 2014. "A mutual information-based k -sample test for discrete distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(9), pages 2011-2027, September.
    16. Antoine, Bertille & Bonnal, Helene & Renault, Eric, 2007. "On the efficient use of the informational content of estimating equations: Implied probabilities and Euclidean empirical likelihood," Journal of Econometrics, Elsevier, vol. 138(2), pages 461-487, June.
    17. McKeague, Ian W. & Zhao, Yichuan, 2002. "Simultaneous confidence bands for ratios of survival functions via empirical likelihood," Statistics & Probability Letters, Elsevier, vol. 60(4), pages 405-415, December.
    18. Ho, Yu-Yun & Weerahandi, Sam, 2007. "Analysis of repeated measures under unequal variances," Journal of Multivariate Analysis, Elsevier, vol. 98(3), pages 493-504, March.
    19. Peter M. Mphekgwana & Yehenew G. Kifle & Chioneso S. Marange, 2024. "Shrinkage Testimator for the Common Mean of Several Univariate Normal Populations," Mathematics, MDPI, vol. 12(7), pages 1-18, April.
    20. Zhao, Yichuan & Zhao, Meng, 2011. "Empirical likelihood for the contrast of two hazard functions with right censoring," Statistics & Probability Letters, Elsevier, vol. 81(3), pages 392-401, March.

    More about this item

    Keywords

    Behrens-Fisher Problem; Empirical Likelihood; Monte Carlo Simulation; Testing for Normality; Size and Power.;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:vic:vicewp:0404. 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: Kali Moon (email available below). General contact details of provider: https://edirc.repec.org/data/devicca.html .

    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.