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Nonparametric tests based on area-statistics

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  • Kraft, Stefan
  • Schmid, Friedrich

Abstract

Area statistics are sample versions of areas occuring in a probability plot of two distribution functions F and G. This paper gives a unified basis for five statistics of this type. They can be used for various testing problems in the framework of the two sample problem for independent observations such as testing equality of distributions against inequality or testing stochastic dominance in one or either direction against nondominance. Though three of the statistics considered have already been suggested in literature, two of them are new and deserve our interest. The finite sample distribution of these statistics can be calculated via recursion formulae. Two tables with critical values of the new statistics are added. The asymptotic distribution of the properly normalized versions of the area statistics are functionals of the Brownian Bridge. The distribution functions and quantiles thereof are obtained by Monte-Carlo-Simulation. Finally, the power of two new tests based on area statistics is compared to the power of tests based on corresponding supremum statistics, i.e. statistics of the Kolmogorov-Smirnov type.

Suggested Citation

  • Kraft, Stefan & Schmid, Friedrich, 2000. "Nonparametric tests based on area-statistics," Discussion Papers in Econometrics and Statistics 2/00, University of Cologne, Institute of Econometrics and Statistics.
    • Handle: RePEc:zbw:ucdpse:200
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    References listed on IDEAS

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    1. Burkhard Heer & Mark Trede, 2004. "Taxation of labour and capital income in an OLG model with home production and endogenous fertility," International Journal of Global Environmental Issues, Inderscience Enterprises Ltd, vol. 4(1/2/3), pages 73-88.
    2. Schmid, Friedrich & Trede, Mark, 1995. "A distribution free test for the two sample problem for general alternatives," Computational Statistics & Data Analysis, Elsevier, vol. 20(4), pages 409-419, October.
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    1. Benoit Dervaux & Gary Ferrier & Herve Leleu & Vivian Valdmanis, 2004. "Comparing French and US hospital technologies: a directional input distance function approach," Applied Economics, Taylor & Francis Journals, vol. 36(10), pages 1065-1081.

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