Effect of extrapolation on coverage accuracy of prediction intervals computed from pareto-type data

Annals of Statistics

Volumn 30, Issue 3, 2002, Pages 875-895

  Hall, Peter ^a   Peng, Liang ^a   Tajvidi, Nader ^b  

^a AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

^b LUND INSTITUTE OF TECHNOLOGY   (Sweden)

Author keywords

Bootstrap; Calibration; Coverage accuracy; Domain of attraction; Exceedence; Extreme value; Generalized Pareto distribution; Peaks over threshold

Indexed keywords

EID: 0036046063     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1028674844     Document Type: Article

References (33)

1. BAI, C. and OLSHEN, R. A. (1988). Comment on "Theoretical comparison of bootstrap confidence intervals," by P. Hall. Ann. Statist. 16 953-956.
2. BAI, C., BICKEL, P. J. and OLSHEN, R. A. (1990). Hyperaccuracy of bootstrap based prediction. In Probability in Banach Spaces VII (E. Eberlein, J. Kuelbs and M. B. Marcus, eds.) 31-42. Birkhäuser, Boston.
3. BARNARD, G. A. (1986). Comment on "Predictive likelihood inference with applications," by R. W. Butler. J. Roy. Statist. Soc. Ser. B 48 27-28.
4. BARNDORFF-NIELSEN, O. E. and COX, D. R. (1994). Inference and Asymptotics. Chapman and Hall, London.
5. BERAN, R. (1990). Refining bootstrap simultaneous confidence sets. J. Amer. Statist. Assoc. 85 417-426.
6. BERAN, R. (1992). Designing bootstrap prediction regions. In Bootstrapping and Related Techniques (K. H. Jöckel, G. Rothe and W. Sendler, eds.) 23-30. Springer, Berlin.
7. BJøRNSTAD, J. F. (1990). Predictive likelihood: a review (with discussion). Statist. Sci. 5 242-265.
8. BUTLER, R. W. (1986). Predictive likelihood inference with applications (with discussion). J. Roy. Statist. Soc. Ser. B 48 1-38.
9. CSÖRGO, S., DEHEUVELS, P. and MASON, D. (1985). Kernel estimates of the tail index of a distribution. Ann. Statist. 13 1050-1077.
10. DAVIS, R. and RESNICK, S. (1984). Tail estimates motivated by extreme value theory. Ann. Statist. 12 1467-1487.
11. DAVISON, A. C. (1984). Modelling excesses over high thresholds, with an application. In Statistical Extremes and Applications (J. Tiago de Oliveira, ed.) 461-482. Reidel, Dordrecht.
12. DAVISON, A. C. (1986). Approximate predictive likelihood. Biometrika 73 323-332.
13. DAVISON, A. C. and SMITH, R. L. (1990). Models for exceedences over high thresholds (with discussion). J. Roy. Statist. Soc. Ser. B 52 393-442.
14. EMBRECHTS, P., KLÜPPELBERG, C. and MIKOSCH, T. (1997). Modelling Extremal Events. Springer, Berlin.
15. FEUERVERGER, A. and HALL, P. (1999). Estimating a tail exponent by modelling departure from a Pareto distribution. Ann. Statist. 27 760-781.
16. GRIMSHAW, S. D. (1993). Computing maximum likelihood estimates for the generalized Pareto distribution. Technometrics 35 185-191.
17. HALL, P. (1992). The Bootstrap and Edgeworth Expansion. Springer, New York.
18. HALL, P., PENG, L. and TAJVIDI, N. (1999). On prediction intervals based on predictive likelihood or bootstrap methods. Biometrika 86 871-880.
19. HILL, B. M. (1975). A simple general approach to inference about the tail of a distribution. Ann. Statist. 3 1163-1174.
20. HOSKING, J. R. M. and WALLIS, J. R. (1987). Parameter and quantile estimation for the generalized Pareto distribution. Technometrics 29 339-349.
21. LEADBETTER, M. R. (1991). On a basis for "peaks over threshold" modeling. Statist. Probab. Lett. 12 357-362.
22. MOHARRAM, S. H., GOSAIN, A. K. and KAPOOR, P. N. (1993). A comparative study for the estimators of the generalized Pareto distribution. J. Hydrology 150 169-185.
23. REISS, R.-D. and THOMAS, M. (1997). Statistical Analysis of Extreme Values, with Applications to Insurance, Finance, Hydrology and Other Fields. Birkhäuser, Basel.
24. ROOTZÉN, H. and TAJVIDI, N. (1997). Extreme value statistics and wind storm losses: a case study. Scand. Actuarial J. 70-94.
25. ROSBJERG, D., MADSEN, H. and RASMUSSEN, P. F. (1992). Prediction in partial duration series with generalized Pareto-distributed exceedences. Water Resources Research 28 3001-3010.
26. RYTGAARD, M. (1990). Estimation in the Pareto distribution. Astin Bull. 20 201-216.
27. SMITH, R. L. (1984). Threshold methods for sample extremes. In Statistical Extremes and Applications (J. Tiago de Oliveira, ed.) 621-638. Reidel, Dordrecht.
28. SMITH, R. L. (1985). Maximum likelihood estimation in a class of nonregular cases. Biometrika 72 67-90.
29. SMITH, R. L. (1987). Estimating tails of probability distributions. Ann. Statist. 15 1174-1207.
30. SMITH, R. L. (1989). Extreme value analysis of environmental time series: an application to trend detection in ground-level ozone (with discussion). Statist. Sci. 4 367-393.
31. STINE, R. A. (1985). Bootstrap prediction intervals for regression. J. Amer. Statist. Assoc. 80 1026-1031.
32. ZIPF, G. K. (1941). National Unity and Disunity: The Nation as a Bio-Social Organism. Principia Press, Bloomington, IN.
33. ZIPF, G. K. (1949). Human Behavior and the Principle of Least Effort: An Introduction to Human Ecology. Addison-Wesley, Cambridge, MA.