Nonparametric tests based on area-statistics

Arbeitspapier

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.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: Discussion Papers in Statistics and Econometrics ; No. 2/00

Classification and Topics

• Classification: Wirtschaft
• Subject: Area Statistics ; P-P-Plot ; Functionals of Brownian Bridge ; Monte Carlo Simulation ; Nonparametric Tests ; Recursion Formulae

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Kraft, Stefan ; Schmid, Friedrich
• Event: Veröffentlichung
• (who): University of Cologne, Seminar of Economic and Social Statistics
• (where): Cologne
• (when): 2000

Further information

• Handle: http://hdl.handle.net/10419/45478
• Last update: 10.03.2025, 11:42 AM CET