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Keywords:

  • bootstrap;
  • crossing quantile curves;
  • monotone rearrangements;
  • non-parametric analysis of covariance;
  • quantile regression;
  • robustness

Abstract.  We consider the problem of testing the equality of J quantile curves from independent samples. A test statistic based on an L2-distance between non-crossing non-parametric estimates of the quantile curves from the individual samples is proposed. Asymptotic normality of this statistic is established under the null hypothesis, local and fixed alternatives, and the finite sample properties of a bootstrap-based version of this test statistic are investigated by means of a simulation study.