City Research Online

Abstract

In this thesis, we focus on the goodness-of-fit (GoF) testing problem. Although there are a number of classical GoF tests proposed in the literature, there is no ‘best’ test that suits all purposes and possesses all the desirable properties. In this thesis, we investigate in detail the properties of two of these classical tests, namely the Kolmogorov-Smirnov and the Kuiper tests, and provide efficient and exact numerical methods to compute their p-values. As known, the latter tests are ordinal and that affects their power especially in the tails. Furthermore, we propose a new H test based on the Hausdorff distance that depends on both the ordinate and abscissa coordinates. As a result of that and of the fact that it is location invariant but scale dependent, we are able to show that its power can be optimized by appropriately selecting the scale coefficient. We illustrate the enhanced power of the H test in numerous numerical examples both in the one-sample univariate and in the two-sample multivariate settings. More precisely, we show that the H test outperforms classical alternatives like Kolmogorov-Smirnov (KS), Cramer-von Mises (CvM) and Anderson-Darling (AD) in terms of power in the univariate case, and also the Ball Divergence, Maximum Mean Discrepancy, Cross Match, the Nearest Neighbor, and some other tests in the bivariate case. Last but not least, we investigate the theoretical properties of the H test and its p-values both for finite samples and asymptotically. We further provide useful results that allow the numerical evaluation of the H test, its p-values, exact Bahadur slope and asymptotic power.

Publication Type:	Thesis (Doctoral)
Subjects:	H Social Sciences > HA Statistics Q Science > QA Mathematics
Departments:	Bayes Business School Bayes Business School > Bayes Business School Doctoral Theses Doctoral Theses

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