Journal of the Korean Statistical Society

The Korean Statistical Society (한국통계학회)
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Tests of Hypotheses in Multiple Samples based on Penalized Disparities

  • Park, Chanseok (Department of Mathematical Sciences, Clemson University) ;
  • Ayanendranath Basu (Applied Statistics Unit, Indian Statistical Institute) ;
  • Ian R. Harris (Department of Mathematics and Statistics, Northern Arizona University)
  • Published : 2001.09.01
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Abstract

Robust analogues of the likelihood ratio test are considered for testing of hypotheses involving multiple discrete distributions. The test statistics are generalizations of the Hellinger deviance test of Simpson(1989) and disparity tests of Lindsay(1994), obtained by looking at a 'penalized' version of the distances; harris and Basu (1994) suggest that the penalty be based on reweighting the empty cells. The results show that often the tests based on the ordinary and penalized distances enjoy better robustness properties than the likelihood ratio test. Also, the tests based on the penalized distances are improvements over those based on the ordinary distances in that they are much closer to the likelihood ratio tests at the null and their convergence to the x$^2$ distribution appears to be dramatically faster; extensive simulation results show that the improvement in performance of the tests due to the penalty is often substantial in small samples.

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References

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