Extension of the One-Sample Kolmogorov-Smirnov Test
Vol. 33 (2026), No. 2, Page 127–160.
Komaba, A.; Johno, H.; Nakamoto, K.
Extension of the One-Sample Kolmogorov-Smirnov Test
[Full Article (PDF)] [MathSciNet Review (HTML)] [MathSciNet Review (PDF)]
Abstract:
We propose here a new goodness-of-fit test, named the one-sample OVL-$q$ test ($q=1, 2,\ldots$), which can be considered an extension of the one-sample Kolmogorov-Smirnov test and the Kuiper test (equivalent to the one-sample OVL-$1$ test and OVL-$2$ test, respectively). We described the asymptotic distribution of the one-sample OVL-$q$ test statistic ($q=1, 2,\ldots$) using a Brownian bridge. We further conducted numerical experiments and demonstrated that the one-sample OVL-$3$ test can sometimes exceed the detection power of conventional goodness-of-fit tests, including the one-sample KS test and the Kuiper test.
Keywords: Nonparametric statistics, Kolmogorov-Smirnov test, Kuiper test, one-sample testing
Mathematics Subject Classification (2020): Primary 62G10; Secondary 62G20, 62-04.
Received: 2024-11-07
