Milan Stehlik, Zdenek Fabian, Lubos Strelec,
"Small Sample Robust Testing for Normality against Pareto Tails"
, in Taylor & Francis Group, in Communications in Statistics - Simulation and Computation, Serie 41, Vol. 7, Seite(n) 1167-1194, 2012
Small Sample Robust Testing for Normality against Pareto Tails
Sprache des Titels:
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.
Sprache der Kurzfassung:
Communications in Statistics - Simulation and Computation