Tsai, Yu-Ling; Dupuis, Debbie J.; Murdoch, Duncan J. A robust test for asymptotic independence of bivariate extremes. (English) Zbl 1440.62173 Statistics 47, No. 1, 172-183 (2013). Summary: We show that the existing tests for asymptotic independence are sensitive to outliers. A robust test is proposed. The new test is made stable under contamination through a shrinkage scheme. Simulations show that the new test performs well in the presence of contaminated data while maintaining good properties when there is no contamination. An application to real data shows the added value of our new robust approach. Cited in 1 Document MSC: 62G32 Statistics of extreme values; tail inference 62G35 Nonparametric robustness 62H15 Hypothesis testing in multivariate analysis 62G20 Asymptotic properties of nonparametric inference Keywords:asymptotic independence testing; contamination; multivariate extremes; robustness; shrinkage scheme PDFBibTeX XMLCite \textit{Y.-L. Tsai} et al., Statistics 47, No. 1, 172--183 (2013; Zbl 1440.62173) Full Text: DOI References: [1] Sibuya M., Ann. Inst. Statist. Math. 11 pp 195– (1960) · Zbl 0095.33703 · doi:10.1007/BF01682329 [2] Dupuis D. J., Extremes 4 pp 315– (2001) · Zbl 1023.62056 · doi:10.1023/A:1016540012032 [3] Gumbel E. J., J. Amer. Statist. Assoc. 59 pp 794– (1964) · doi:10.1080/01621459.1964.10480728 [4] Tawn J. A., Biometrika 75 pp 397– (1988) · Zbl 0653.62045 · doi:10.1093/biomet/75.3.397 [5] Ledford A., Biometrika 83 pp 169– (1996) · Zbl 0865.62040 · doi:10.1093/biomet/83.1.169 [6] Peng L., Stat. Probab. Lett. 43 pp 399– (1999) · Zbl 0958.62049 · doi:10.1016/S0167-7152(98)00280-6 [7] Draisma G., Bernoulli 10 pp 251– (2004) · Zbl 1058.62043 · doi:10.3150/bj/1082380219 [8] Ramos A., Extremes 8 pp 5– (2005) · Zbl 1091.62050 · doi:10.1007/s10687-005-4857-4 [9] Zhang Z., Adv. Econom. Econom. Anal. Financial Econ. Time Ser. Part B 20 pp 317– (2006) [10] Zhang Z., Ann. Stat. 36 pp 1007– (2008) · Zbl 1133.62041 · doi:10.1214/009053607000000866 [11] Field C. A., Int. Statist. Rev. 62 pp 405– (1994) · Zbl 0825.62428 · doi:10.2307/1403770 [12] Murdoch D., Amer. Statist. 62 pp 242– (2008) · Zbl 05680803 · doi:10.1198/000313008X332421 [13] Tsai , Y. 2006 . ” Using robust and Bayesian methods to assess asymptotic independence in extreme values ” . Ontario : University of Western . Ph.D. thesis [14] Joe H., Multivariate Models and Dependence Concepts (1997) · Zbl 0990.62517 · doi:10.1201/b13150 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.