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Robust tests for the equality of two normal means based on the density power divergence

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  • A. Basu
  • A. Mandal
  • N. Martin
  • L. Pardo

Abstract

Statistical techniques are used in all branches of science to determine the feasibility of quantitative hypotheses. One of the most basic applications of statistical techniques in comparative analysis is the test of equality of two population means, generally performed under the assumption of normality. In medical studies, for example, we often need to compare the effects of two different drugs, treatments or preconditions on the resulting outcome. The most commonly used test in this connection is the two sample $$t$$ t test for the equality of means, performed under the assumption of equality of variances. It is a very useful tool, which is widely used by practitioners of all disciplines and has many optimality properties under the model. However, the test has one major drawback; it is highly sensitive to deviations from the ideal conditions, and may perform miserably under model misspecification and the presence of outliers. In this paper we present a robust test for the two sample hypothesis based on the density power divergence measure (Basu et al. in Biometrika 85(3):549–559, 1998 ), and show that it can be a great alternative to the ordinary two sample $$t$$ t test. The asymptotic properties of the proposed tests are rigorously established in the paper, and their performances are explored through simulations and real data analysis. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • A. Basu & A. Mandal & N. Martin & L. Pardo, 2015. "Robust tests for the equality of two normal means based on the density power divergence," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(5), pages 611-634, July.
    • Handle: RePEc:spr:metrik:v:78:y:2015:i:5:p:611-634
    DOI: 10.1007/s00184-014-0518-4
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    References listed on IDEAS

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    1. A. Basu & A. Mandal & N. Martin & L. Pardo, 2013. "Testing statistical hypotheses based on the density power divergence," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(2), pages 319-348, April.
    2. Fujisawa, Hironori & Eguchi, Shinto, 2008. "Robust parameter estimation with a small bias against heavy contamination," Journal of Multivariate Analysis, Elsevier, vol. 99(9), pages 2053-2081, October.
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    1. 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.
    2. N. Balakrishnan & N. Martín & L. Pardo, 2017. "Empirical phi-divergence test statistics for the difference of means of two populations," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 101(2), pages 199-226, April.

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