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Small Sample Robust Testing for Normality against Pareto Tails
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SYSNO ASEP 0376157 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Small Sample Robust Testing for Normality against Pareto Tails Author(s) Stehlík, M. (AT)
Fabián, Zdeněk (UIVT-O) SAI, RID
Střelec, L. (CZ)Source Title Communications in Statistics - Simulation and Computation. - : Taylor & Francis - ISSN 0361-0918
Roč. 41, č. 7 (2012), s. 1167-1194Number of pages 28 s. Language eng - English Country US - United States Keywords consistency ; Hill estimator ; t-Hill estimator ; location functional ; Pareto tail ; power comparison ; returns ; robust tests for normality Subject RIV BB - Applied Statistics, Operational Research CEZ AV0Z10300504 - UIVT-O (2005-2011) UT WOS 000304853800018 EID SCOPUS 84859857216 DOI 10.1080/03610918.2012.625849 Annotation The aim of this article is to introduce the general form (so called RT class) of the robust and classical Jarque–Bera (JB) test based on the location functional. We introduce the two-step procedure which is optimal for testing against the individual or contaminated Pareto alternative. As a reference for such a contamination we consider different Pareto distributions. We also give practical guidelines for robust testing for normality against short- and heavy-tailed alternatives. We concentrate mainly on simulation results for moderate and small samples. However, we also prove consistency and asymptotic distribution for introduced tests. We show that as the suitable measure of nominal level of Pareto tail parameter we may take the t- Hill estimator introduced in the article. To guarantee the consistency of the whole procedure, we also prove the consistency of t-Hill estimator. The introduced general class of robust tests of the normality is illustrated at the selected datasets of financial time series. Workplace Institute of Computer Science Contact Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Year of Publishing 2013
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