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On testing homogeneity of variances for nonnormal models using entropy

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Abstract

This paper deals with testing equality of variances of observations in the different treatment groups assuming treatment effects are fixed. We study the distribution of a test statistic which is known to perform comparably well with other statistics for the same purpose under normality. The statistic we consider is based on Shannon’s entropy for a distribution function. We will derive the asymptotic expansion for the distribution of the test statistic based on Shannon’s entropy under nonnormality and numerically examine its performance in comparison with the modified likelihood ratio criteria for normal and some nonnormal populations.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH, 43403, USA

    Arjun K. Gupta

  2. Department of Mathematical Sciences, University of Montana, Missoula, MT, 59812, USA

    Solomon W. Harrar

  3. Department of Statistics and Operations Research, Complutense University of Madrid, 28040, Madrid, Spain

    Leandro Pardo

Authors
  1. Arjun K. Gupta
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  2. Solomon W. Harrar
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  3. Leandro Pardo
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Correspondence to Arjun K. Gupta.

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Gupta, A.K., Harrar, S.W. & Pardo, L. On testing homogeneity of variances for nonnormal models using entropy. Stat. Meth. & Appl. 16, 245–261 (2007). https://doi.org/10.1007/s10260-007-0055-7

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  • DOI: https://doi.org/10.1007/s10260-007-0055-7

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