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Smooth Test For Testing Equality Of Two Densities


  • Zhijie Xiao
  • Anil K. Bera
  • Aurobindo Ghosh


It has been a conventional wisdom that the two-sample version of the goodness-of-fit test like the Kolmogorov-Smirnov, Cramér-von Mises and Anderson-Darling tests fail to have good power particularly against very specific alternatives. We show that a modified version of Neyman Smooth test that can also be derived as a score test based on the empirical distribution functions obtained from the two samples remarkably improves the detection of directions of departure. We can identify deviations in different moments like the mean, variance, skewness or kurtosis terms using the Ratio Density Function. We derive a bound on the relative sample sizes of the two samples for a consistent test and an "optimal" choice range of the sample sizes to ensure minimal size distortion in finite samples. We apply our procedure to compare the age distributions of employees insured with small employers

Suggested Citation

  • Zhijie Xiao & Anil K. Bera & Aurobindo Ghosh, 2004. "Smooth Test For Testing Equality Of Two Densities," Econometric Society 2004 Far Eastern Meetings 714, Econometric Society.
  • Handle: RePEc:ecm:feam04:714

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    More about this item


    Empirical distribution function; Locally optimal tests; score test; sample size selection; smooth test; two-sample test; simulation study;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General


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