%0 Generic %1 eiger2013calibrated %A Eiger, Amit Moscovich %A Nadler, Boaz %A Spiegelman, Clifford %D 2013 %K KStest %T The Calibrated Kolmogorov-Smirnov Test %U http://arxiv.org/abs/1311.3190 %X Continuous goodness-of-fit (GOF) is a classical hypothesis testing problem in statistics. Despite numerous suggested methods, the Kolmogorov-Smirnov (KS) test is, by far, the most popular GOF test used in practice. Unfortunately, it lacks power at the tails, which is important in many practical applications. In this paper we make two main contributions: First, we propose the \em Calibrated KS (CKS) statistic, a novel test statistic based on the following principle: Instead of looking for the largest deviation between the empirical and assumed distributions, as in the original KS test, we search for the deviation which is most statistically significant. By construction, the resulting CKS test achieves good detection power throughout the entire range of the distribution. Second, we derive a novel computationally efficient method to calculate $p$-values for a broad family of one-sided GOF tests, including the one-sided version of CKS, as well as the Higher Criticism and the Berk-Jones tests. We conclude with some simulation results comparing the power of CKS to several other tests.

@misc{eiger2013calibrated, abstract = {Continuous goodness-of-fit (GOF) is a classical hypothesis testing problem in statistics. Despite numerous suggested methods, the Kolmogorov-Smirnov (KS) test is, by far, the most popular GOF test used in practice. Unfortunately, it lacks power at the tails, which is important in many practical applications. In this paper we make two main contributions: First, we propose the {\em Calibrated KS} (CKS) statistic, a novel test statistic based on the following principle: Instead of looking for the largest deviation between the empirical and assumed distributions, as in the original KS test, we search for the deviation which is most {\em statistically significant}. By construction, the resulting CKS test achieves good detection power throughout the entire range of the distribution. Second, we derive a novel computationally efficient method to calculate $p$-values for a broad family of one-sided GOF tests, including the one-sided version of CKS, as well as the Higher Criticism and the Berk-Jones tests. We conclude with some simulation results comparing the power of CKS to several other tests.}, added-at = {2014-02-02T21:25:29.000+0100}, author = {Eiger, Amit Moscovich and Nadler, Boaz and Spiegelman, Clifford}, biburl = {https://www.bibsonomy.org/bibtex/25dd0b8eef0d66c33234f82f5b8aa1ae4/marsianus}, description = {[1311.3190] The Calibrated Kolmogorov-Smirnov Test}, interhash = {bb0a75b1f842bb1c84152c2731aef97e}, intrahash = {5dd0b8eef0d66c33234f82f5b8aa1ae4}, keywords = {KStest}, note = {cite arxiv:1311.3190}, timestamp = {2014-02-02T21:25:29.000+0100}, title = {The Calibrated Kolmogorov-Smirnov Test}, url = {http://arxiv.org/abs/1311.3190}, year = 2013 }