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Small Sample Robust Testing for Normality against Pareto Tails

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    0376157 - UIVT-O 2013 RIV US eng J - Journal Article
    Stehlík, M. - Fabián, Zdeněk - Střelec, L.
    Small Sample Robust Testing for Normality against Pareto Tails.
    Communications in Statistics: Simulation and Computation. Roč. 41, č. 7 (2012), s. 1167-1194. ISSN 0361-0918
    Grant - others:Aktion(CZ-AT) 51p7, 54p21, 50p14, 54p13
    Institutional research plan: CEZ:AV0Z10300504
    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
    Impact factor: 0.295, year: 2012

    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.
    Permanent Link: http://hdl.handle.net/11104/0208638