Small Improvement to the Kolmogorov-Smirnov Test
نویسندگان
چکیده
The Kolmogorov-Smirnov (K-S) test is widely used as a goodness-of-fit test. This thesis consists of two parts to describe ways to improve the classical K-S test in both 1-dimensional and 2-dimensional data. The first part is about how to improve the accuracy of the classical K-S goodness-of-fit test in 1-dimensional data. We replace the p-values estimated by the asymptotic distribution with near-exact p-values. In the second part, we propose two new methods to increase power of the widely used 2-dimensional two-sample Fasano and Franceschini test. Simulation studies show the new methods are significantly more powerful than the Fasano and Franceschini’s test. INDEX WORDS: K-S test, Cramér-von Mises test, 2-Dimensional K-S test, Goodness-of-fit, Nearexact distribution of K-S statistics SMALL IMPROVEMENT TO THE KOLMOGOROV-SMIRNOV TEST
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