Nonparametric tests based on area-statistics

Stefan Kraft and Friedrich Schmid

No 2/00, Discussion Papers in Econometrics and Statistics from University of Cologne, Institute of Econometrics and Statistics

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.

Keywords: Area Statistics; P-P-Plot; Functionals of Brownian Bridge; Monte Carlo Simulation; Nonparametric Tests; Recursion Formulae (search for similar items in EconPapers)
Date: 2000
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.econstor.eu/bitstream/10419/45478/1/657510653.pdf (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:zbw:ucdpse:200

Access Statistics for this paper

More papers in Discussion Papers in Econometrics and Statistics from University of Cologne, Institute of Econometrics and Statistics Contact information at EDIRC.
Bibliographic data for series maintained by ZBW - Leibniz Information Centre for Economics ().