Estimating the extremal index through the tail dependence concept

• Autorzy: Marta Ferreira
• Języki publikacji: EN

Abstrakty

EN

The extremal index Θ is an important parameter in extreme value analysis when extending results from independent and identically distributed sequences to stationary ones. A connection between the extremal index and the tail dependence coefficient allows the introduction of new estimators. The proposed ones are easy to compute and we analyze their performance through a simulation study. Comparisons with other existing methods are also presented. Case studies within environment are considered in the end.

Słowa kluczowe

EN

extreme value theory; extremal index; tail dependence coefficient

Kategorie tematyczne

• 62G32: Statistics of extreme values; tail inference

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae Probability and Statistics
• Rocznik: 2015
• Tom: 35
• Numer: 1-2
• Strony: 61-74

Daty

wydano

2015

otrzymano

2015-04-01

Twórcy

autor

Marta Ferreira

• Center of Mathematics, University of Minho, Portugal

Bibliografia

• [1] M.A. Ancona-Navarrete and J.A. Tawn, A comparison of methods for estimating the extremal index, Extremes 3 (2000), 5-38.
• [2] J. Beirlant, Y. Goegebeur, J. Segers and J. Teugels, Statistics of Extremes: Theory and Application 9John Wiley, 2004).
• [3] P. Capéraà, A.L. Fougères and C. Genest, A nonparametric estimation procedure for bivariate extreme value copulas, Biometrika 84 (1997), 567-577.
• [4] M.R. Chernick, T. Hsing and W.P. McCormick, Calculating the extremal index for a class of stationary sequences, Adv. Appl. Probab. 23 (1991), 835-850.
• [5] S.G. Coles, An Introduction to Statistical Modelling of Extreme Values (London, Springer, 2001).
• [6] M. Ferreira, Nonparametric estimation of the tail dependence coefficient, REVSTAT 11 (2013), 1-16.
• [7] M. Ferreira and H. Ferreira, On extremal dependence: some contributions, TEST 21 (2012a), 566-583.
• [8] H. Ferreira and M. Ferreira, On extremal dependence of block vectors, Kybernetika 48 (2012b), 988-1006.
• [9] C.A. Ferro and J. Segers, Inference for clusters of extremes, J.R. Stat. Soc. Ser. B Stat. Methodol. 65 (2003), 545-556.
• [10] G. Frahm, M. Junker and R. Schmidt, Estimating the tail-dependence coefficient: properties and pitfalls, Insurance Math. Econom. 37 (2005), 80-100.
• [11] C. Genest and J. Segers J., Rank-based inference for bivariate extreme-value copulas, Ann. Statist. 37 (2009), 2990-3022.
• [12] M.I. Gomes, A. Hall and C. Miranda, Subsampling techniques and the jackknife methodology in the estimation of the extremal index, J. Stat. Comput. Simul. 52 (2008), 2022-2041.
• [13] T. Hsing, J. Husler and M.R. Leadbetter, On the exceedance point process for a stationary sequence, Probab. Theory Related Fields 78 (1988), 97-112.
• [14] M.R. Leadbetter, Extremes and local dependence in stationary sequences, Z. Wahrsch. Ver. Geb. 65 (1983), 291-306.
• [15] R.M. Loynes, Extreme Values in Uniformly Mixing Stationary Stochastic Processes, Annals of Mathematical Statistics 36 (1965), 993-999.
• [16] S. Nandagopalan, Multivariate extremes and estimation of the extremal index (Ph.D. Thesis, University of North Carolina at Chapel Hill, 1990).
• [17] G.L. O'Brien, The maximum term of uniformly mixing stationary sequences, Z. Wahrsch. Ver. Geb. 30 (1974), 57-63.
• [18] R.D. Reiss, M. Thomas, Statistical analysis of extreme values with applications to insurance, finance, hydrology and other fields (Birkhäuser, Basel, 2007).
• [19] R. Schmidt and U. Stadtmüller, Nonparametric estimation of tail dependence, Scandinavian J. Statist. 33 (2006), 307-335.
• [20] J.R. Sebastiăo, A.P. Martins, H. Ferreira and L.Pereira, Estimating the upcrossings index, TEST 22 (2013), 549-579.
• [21] M. Sibuya, Bivariate extreme statistics, Ann. Inst. Stat. Math. 11 (1960), 195-210.
• [22] M. Süveges, Likelihood estimation of the extremal index, Extremes 10 (2007), 41-55.

Identyfikatory

DOI

10.7151/dmps.1173