Generalized Cramér-von Mises goodness-of-fit tests for multivariate distributions

  • Authors:
  • Sung Nok Chiu;Kwong Ip Liu

  • Affiliations:
  • Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong;Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong

  • Venue:
  • Computational Statistics & Data Analysis
  • Year:
  • 2009

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Abstract

A class of statistics for testing the goodness-of-fit for any multivariate continuous distribution is proposed. These statistics consider not only the goodness-of-fit of the joint distribution but also the goodness-of-fit of all marginal distributions, and can be regarded as generalizations of the multivariate Cramer-von Mises statistic. Simulation shows that these generalizations, using the Monte Carlo test procedure to approximate their finite-sample p-values, are more powerful than the multivariate Kolmogorov-Smirnov statistic.