Skip to main content
Log in

Comparing Two Independent Populations Using a Test Based on Empirical Likelihood and Trimmed Means

  • Published:
Lithuanian Mathematical Journal Aims and scope Submit manuscript

Abstract

We develop a new robust empirical likelihood-based test for comparing the trimmed means of two independent populations. The simulation results indicate that the test has asymptotically correct level under various data distributions and controls the Type I error adequately for medium-size samples. For nonnormal data distributions, the power of the test is comparable to robust alternatives like Yuen’s test for the trimmed means and considerably exceeds that of the tests based on the means. In small sample settings the test version for the difference of 10% trimmed means exhibits robustness to the combined presence of nonnormality and heterogeneity.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. B.C. Arnold, N. Balakrishnan, and H.N. Nagaraja, A First Course in Order Statistics, Classics in Applied Mathematics, SIAM, Philadelphia, 2008.

    Book  Google Scholar 

  2. J.V. Bradley, Robustness?, Br. J. Math. Stat. Psychol., 31:144–152, 1978.

    Article  MathSciNet  Google Scholar 

  3. G. Casella and R.L. Berger, Statistical Inference, Duxbury Advanced Series, Brooks/Cole Publishing Company, 1990.

    MATH  Google Scholar 

  4. E. Cers and J. Valeinis, EL: Two-sample Empirical Likelihood, R package version 1.0, 2011, https://CRAN.R-project.org/package=EL.

    Google Scholar 

  5. N.A. Cressie and H.J. Whitford, How to use the two sample t-test, Biom. J., 28(2):131–148, 1986.

    Article  MathSciNet  Google Scholar 

  6. R. Fried and H. Dehling, Robust nonparametric tests for the two-sample location problem, Stat.Methods Appl., 20(2): 409–422, 2011.

    Article  MathSciNet  Google Scholar 

  7. H.J. Keselman, R.R. Wilcox, A.R. Othman, and K. Fradette, Trimming, transforming statistics, and bootstrapping: Circumventing the biasing effects of heterescedasticity and nonnormality, J.Mod. Appl. Stat.Methods, 1(2):288–309, 2002.

    Article  Google Scholar 

  8. L.M. Lix and H.J. Keselman, To trim or not to trim: Tests of location equality under heteroscedasticity and nonnormality, Educ. Psychol. Meas., 58(3):409–429, 1998.

    Article  Google Scholar 

  9. A. Marazzi, Bootstrap tests for robust means of asymmetric distributions with unequal shapes, Comput. Stat. Data Anal., 49:503–528, 2002.

    Article  MathSciNet  Google Scholar 

  10. R.A. Maronna, R.D. Martin, V.J. Yohai, and M. Salibián-Barrera, Robust Statistics: Theory and Methods (with R), 2nd ed., Wiley, New York, 2018.

    Book  Google Scholar 

  11. A.B. Owen, Empirical likelihood ratio confidence intervals for a single functional, Biometrika, 75(2):237–249, 1988.

    Article  MathSciNet  Google Scholar 

  12. A.B. Owen, Empirical Likelihood, Chapman & Hall/CRC Press, New York, 2001.

    Book  Google Scholar 

  13. G. Qin and M. Tsao, Empirical likelihood ratio confidence interval for the trimmed mean, Commun. Stat., Theory Methods, 31(12):2197–2208, 2002.

    Article  MathSciNet  Google Scholar 

  14. J. Qin and J. Lawless, Empirical likelihood and general estimating equations, Ann. Stat., 22:300–325, 1994, https://doi.org/10.1214/aos/1176325370.

    Article  MathSciNet  MATH  Google Scholar 

  15. Y.S. Qin and L.C. Zhao, Empirical likelihood ratio confidence intervals for various differences of two populations, Syst. Sci. Math. Sci., 13(1):23–30, 2000.

    MathSciNet  MATH  Google Scholar 

  16. S.M. Stigler, The asymptotic distribution of the trimmed mean, Ann. Stat., 1(3):472–477, 1973.

    Article  MathSciNet  Google Scholar 

  17. J. Valeinis, E. Cers, and J. Cielens, Two-sample problems in statistical data modelling, Math. Model. Anal., 15:137–151, 2010.

    Article  MathSciNet  Google Scholar 

  18. M. Velina, J. Valeinis, L. Greco, and G. Luta, Empirical likelihood-basedANOVA for trimmed means, Int. J. Environ. Res. Public Health, 13(10):1–13, 2016, https://doi.org/10.3390/ijerph13100953.

    Article  Google Scholar 

  19. M. Velina, J. Valeinis, and G. Luta, Likelihood-based inference for the difference of two location parameters using smoothed M-estimators, J. Stat. Theory Pract., 13:34, 2019, https://doi.org/10.1007/s42519-019-0037-8.

  20. B.L. Welch, The generalization of “Student’s” problem when several different population variances are involved, Biometrika, 34(1):28–35, 1947.

    MathSciNet  MATH  Google Scholar 

  21. R.R. Wilcox, Introduction to Robust Estimation and Hypothesis Testing, 3rd ed., Academic Press, Boston, 2012.

    MATH  Google Scholar 

  22. S.S. Wilks, The large-sample distribution of the likelihood ratio for testing composite hypotheses, Ann. Math. Stat., 9:60–62, 1938.

    Article  Google Scholar 

  23. K.K. Yuen, The two-sample trimmed t for unequal population variances, Biometrika, 61(1):165–170, 1974.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Māra Delesa-Vēliņa.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Delesa-Vēliņa, M., Valeinis, J. & Luta, G. Comparing Two Independent Populations Using a Test Based on Empirical Likelihood and Trimmed Means. Lith Math J 61, 199–216 (2021). https://doi.org/10.1007/s10986-021-09516-x

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10986-021-09516-x

Keywords

Navigation