Subsampling techniques and the Jackknife methodology in the estimation of the extremal index

Computational Statistics and Data Analysis

Volumn 52, Issue 4, 2008, Pages 2022-2041

  Gomes, M Ivette ^a   Hall, Andreia ^b   Miranda, M Cristina ^b  

^a UNIVERSITY OF LISBON   (Portugal)

^b UNIVERSITY OF AVEIRO   (Portugal)

Author keywords

Extremal index; Generalized jackknife; Statistics of extremes; Subsampling techniques

Indexed keywords

ASYMPTOTIC ANALYSIS; CLUSTER ANALYSIS; DISTRIBUTION FUNCTIONS; POISSON DISTRIBUTION;

DISTRIBUTED RANDOM VARIABLES; EXTREMAL INDEXES; JACKKNIFE METHODOLOGIES; LIMITING POINT PROCESS; STATISTICS OF EXTREMES; SUBSAMPLING TECHNIQUES;

INDEXING (OF INFORMATION);

EID: 35748939728     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2007.06.023     Document Type: Article

References (30)

1. Alonso A.M., and Maharaj E.A. Comparison of time series using subsampling. Comput. Statist. Data Anal. 50 (2006) 2589-2599
2. Alpuim M.T. An extremal markovian sequence. J. Appl. Probab. 26 (1989) 219-232
3. Caeiro F., Gomes M.I., and Pestana D. Direct reduction of bias of the classical Hill estimator. Revstat 3 2 (2005) 113-136
4. Casella G., and Berger R.L. Statistical Inference. second ed (2002), Duxbury Press
5. Chernick M., Hsing T., and McCormick W. Calculating the extremal index for a class of stationary sequences. Adv. in Appl. Probab. 23 (1991) 835-850
6. Drees H., de Haan L., and Resnick S. How to make a Hill plot. Ann. Statist. 28 (2000) 254-274
7. Ferreira H., and Martins A.P. The extremal index of sub-sampled periodic sequences. Revstat 1 (2003) 15-24
8. Gomes M.I., and Figueiredo F. Bias reduction in risk modelling: semi-parametric quantile estimation. Test 15 2 (2006) 375-396
9. Gomes M.I., and Oliveira O. The bootstrap methodology in Statistics of extremes-choice of the optimal sample fraction. Extremes 4 4 (2001) 331-358
10. Gomes M.I., and Pestana D. A sturdy reduced bias extreme quantile (VaR) estimator. J. Amer. Statist. Assoc. 102 477 (2007) 280-292
11. Gomes M.I., and Pestana D. A simple second order reduced bias estimator. J. Statist. Comput. Simulation 77 6 (2007) 487-504
12. Gomes M.I., Martins M.J., and Neves M. Alternatives to a semi-parametric estimator of parameters of rare events-the Jackknife methodology. Extremes 3 3 (2000) 207-229
13. Gomes M.I., Martins M.J., and Neves M. Generalized Jackknife semi-parametric estimators of the tail index. Portugal. Math. 59 4 (2002) 393-408
14. Gomes M.I., Miranda C., and Pereira H. Revisiting the role of the Jackknife methodology in the estimation of a positive tail index. Comm. Statist. Theory Methods 34 (2005) 1-20
15. Gomes M.I., Miranda C., and Viseu C. Reduced bias tail index estimation and the Jackknife methodology. Statist. Neerlandica 61 2 (2007) 243-270
16. Gray H.L., and Schucany W.R. The Generalized Jackknife Statistic (1972), Marcel Dekker, New York
17. de Haan L., Resnick S., Rootzén H., and deVries C. Extremal behaviour of solutions to a stochastic difference equation with applications to ARCH-processes. Stochastic. Process. Appl. 32 (1989) 213-224
18. Hall A. Maximum term of a particular autoregressive sequence with discrete margins. Comm. Statist. Theory Methods 25 4 (1996) 721-736
19. Hsing T., and Leadbetter M.R. On the exceedance point process for a stationary sequence. Probab. Theory Related Fields 78 (1988) 97-112
20. Joe H. Multivariate extreme-value distributions with applications to environmental data. Canad. J. Statist. 22 (1994) 47-64
21. Leadbetter M.R., and Nandagopalan S. On exceedance point processes for stationary sequences under mild oscillation restrictions. In: Hsler J., and Reiss R.-D. (Eds). Extreme Value Theory (1989), Springer, New York 69-80
22. Leadbetter M.R., Lindgren G., and Rootzén H. Extremes and Related Properties of Random Sequences and Series (1983), Springer, New York
23. Martins A.P., and Ferreira H. The extremal index of sub-sampled processes. J. Statist. Plann. Inference 124 (2004) 145-152
24. Nandagopalan, S., 1990. Multivariate extremes and estimation of the extremal index. Ph.D. Thesis, University of North Carolina at Chapel Hill.
25. Reiss, R.-D., Thomas, M., 1997. Statistical Analysis of Extreme Values with Applications to Insurance, Finance, Hydrology and Other Fields. First ed. Birkhäuser Verlag, Basel, Switzerland.
26. Reiss R.-D., and Thomas M. Statistical Analysis of Extreme Values with Applications to Insurance, Finance, Hydrology and Other Fields. Second ed (2001), Birkhäuser Verlag, Basel, Switzerland
27. Reiss, R.-D., Thomas, M., 2007. Statistical Analysis of Extreme Values with Applications to Insurance, Finance, Hydrology and Other Fields. Third ed. Birkhäuser Verlag, Basel, Switzerland.
28. Robinson M.E., and Tawn J.A. Extremal analysis of processes sampled at different frequencies. J. Roy. Statist. Soc. Ser. B 62 (2000) 117-135
29. Scotto M., and Ferreira H. Extremes of deterministic sub-sampled moving averages with heavy-tailed innovations. Appl. Stochastic Models Bus. Ind. 19 (2003) 303-313
30. Scotto M., Turkman K.F., and Anderson C.W. Extremes of some sub-sampled time series. J. Time Ser. Anal. 24 5 (2003) 505-512