A note on the nonparametric test based on theL 1-version of the Cramér-von Mises statistic

Abstract

We consider the test based on theL 1-version of the Cramér-von Mises statistic for the nonparametric two-sample problem. Some quantiles of the exact distribution under H0 of the test statistic are computed for small sample sizes. We compare the test in terms of power against general alternatives to other two-sample tests, namely the Wilcoxon rank sum test, the Smirnov test and the Cramér-von Mises test in the case of unbalanced small sample sizes. The computation of the power is rather complicated when the sample sizes are unequal. Using Monte Carlo power estimates it turns out that the Smirnov test is more sensitive to non stochastically ordered alternatives than the new test. And under location-contamination alternatives the power estimates of the new test and of the competing tests are equal.

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Arrenberg, J. A note on the nonparametric test based on theL 1-version of the Cramér-von Mises statistic. Statistical Papers 37, 95–104 (1996). https://doi.org/10.1007/BF02926575

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Keywords

  • Smirnov Test
  • Null Distribution
  • Statistical Paper
  • General Alternative
  • Mise Statistic