Localized Pearson Goodness-of-Fit Tests

• Activity Number: 418
• Type: Contributed
• Date/Time: Wednesday, August 6, 2003 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Olivier Thas*+ and Jean-Pierre Ottoy
• Companies: University of Ghent and Ghent University
• Keywords: goodness-of-fit ; Pearson chi-square ; Anderson-Darling ; multimodality

Abstract

We propose a new class of consistent goodness-of-fit statistics, $T_{c,n}$, which may be considered as an extension of the Anderson-Darling statistic. The class is indexed by the number of degrees of freedom ($c$) of the Pearson chi-square statistic which is used as the core of the new statistic. In particular, the statistics are defined as the $c$-fold integral of Pearson's chi-square statistic with respect to the hypothesized distribution function. The results of a simulation study indicate good power characteristics, but they also show that the power depends to a large extend on the choice of the index parameter. To overcome this problem, we construct a data-driven version of the test. A simulation study suggests that the data-driven test has good powers against many alternatives. Our results show that an important component of $T_{c,n}$ is a weighted Watson statistic. Based on this observation, we argue that our new tests are particularly powerful for alternatives that deviate from the hypothesized distribution in only a small subset of the support. Finally, we show how the $T_{c,n}$ statistic can be changed to detect multimodality.