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Statistics & Risk Modeling

with Applications in Finance and Insurance

Editor-in-Chief: Stelzer, Robert


Cite Score 2018: 0.85

SCImago Journal Rank (SJR) 2018: 0.354
Source Normalized Impact per Paper (SNIP) 2018: 0.604

Mathematical Citation Quotient (MCQ) 2018: 0.36

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2196-7040
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On preferences of general two-sided tests with applications to Kolmogorov–Smirnov-type tests

Jörg Rahnenführer
Published Online: 2009-09-25 | DOI: https://doi.org/10.1524/stnd.21.2.149.19004

Summary

Power functions of tests for Gaussian shift experiments on infinite dimensional Hilbert spaces usually can not be calculated explicitly. Therefore one analyzes the behavior of such tests in the neighborhood of the null hypothesis. Useful measures to compare the quality of different testing procedures are the gradient of a one-sided and the curvature of a two-sided test in the null hypothesis. Janssen (1995) showed that a principal component decomposition of the curvature exists based on a Hilbert–Schmidt operator. It follows that these tests have only acceptable power for a finite number of directions. In this paper we prove an even stronger general result for Gauss shifts under just mild additional assumptions. A certain optimality property of a one-sided test implicates that for a small level α the corresponding two-sided test acts only in a single direction. The results are applied to Kolmogorov–Smirnov type tests and the signal detection problem.

About the article

Published Online: 2009-09-25

Published in Print: 2003-02-01


Citation Information: Statistics & Decisions/International mathematical Journal for stochastic methods and models, Volume 21, Issue 2/2003, Pages 149–170, ISSN (Print) 0721-2631, DOI: https://doi.org/10.1524/stnd.21.2.149.19004.

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[1]
Arnold Janssen and Hülya Ünlü
Journal of Statistical Planning and Inference, 2008, Volume 138, Number 8, Page 2526
[2]
Christopher S. Withers and Saralees Nadarajah
ESAIM: Probability and Statistics, 2009, Volume 13, Page 283

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