Unbiased goodness-of-fit tests.

Familiar distribution-free goodness-of-fit tests like the Kolmogorov-Smirnov test are all biased tests. In this paper, we show how to compute the bias of any distribution-free goodness-of-fit test that corresponds to a distribution-free confidence band for the cumulative distribution function (CDF). This bias of the Kolmogorov-Smirnov test turns out to be smaller than the biases of other distribution-free goodness-of-fit tests. We also develop a method for obtaining unbiased goodness-of-fit tests, which can then be inverted to obtain unbiased confidence bands for the CDF. Interestingly, only a discrete set of levels are available for the unbiased tests. Our power comparisons show that while removing bias improves the power of a test at some alternatives, it does not improve the overall power properties of the test.

Main Author: Frey, Jesse.
Language: English
Published: 2009
Online Access: http://ezproxy.villanova.edu/login?url=https://digital.library.villanova.edu/Item/vudl:176391