Regression with response distributions of Pareto-type

Computational Statistics and Data Analysis

Volumn 42, Issue 4, 2003, Pages 595-619

  Beirlant, Jan ^a   Goegebeur, Yuri ^a  

^a UNIVERSITY OF LEUVEN   (Belgium)

Author keywords

Exponential regression model; Extreme value index; Generalized residuals; Pareto quantile plot; Profile likelihood function

Indexed keywords

MATHEMATICAL MODELS; MAXIMUM LIKELIHOOD ESTIMATION; PARAMETER ESTIMATION; PARETO PRINCIPLE;

COVARIATE INFORMATION;

REGRESSION ANALYSIS;

REGRESSION;

EID: 0037471446     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-9473(02)00120-2     Document Type: Article

References (29)

1. Barndorff-Nielsen, O.E., Cox, D.R., 1994. Inference and Asymptotics. Chapman & Hall, London.
2. Beirlant, J., Teugels, J.L., Vynckier, P., 1996a. Practical Analysis of Extreme Values. Leuven University Press, Leuven.
3. Beirlant, J., Vynckier, P., Teugels, J.L., 1996b. Excess functions and estimation of the extreme value index. Bernoulli 2, 293-318.
4. Beirlant, J., Goegebeur, Y., Verlaak, R., Vynckier, P., 1998. Burr regression and portfolio segmentation. Insurance: Mathematics and Economics 23, 231-250.
5. Beirlant, J., Dierckx, G., Goegebeur, Y., Matthys, G., 1999. Tail index estimation and an exponential regression model. Extremes 2, 177-200.
6. Bingham, N.H., Goldie, C.M., Teugels, J.L., 1987. Regular Variation. Cambridge University Press, Cambridge.
7. Burr, I.V., 1942. Cumulative frequency functions. Ann. Math. Statist. 13, 215-232.
8. Castillo, E., Hadi, A.S., 1997. Fitting the generalized Pareto distribution to data. J. Amer. Statist. Assoc. 92, 1609-1620.
9. Coles, S., Tawn, J., 1998. Statistical methods for extreme values. A course presented at the 1998 RSS Conference, Strathclyde, September, 1998.
10. Csörgö, S., Viharos, L., 1998. Estimating the tail index. In Szyszkowicz B. (Ed.), Asymptotic Methods in Probability and Statistics, North-Holland, Amsterdam, pp. 833-881.
11. Csörgö, S., Deheuvels, P., Mason, D.M., 1985. Kernel estimates of the tail index of a distribution. Ann. Statist. 13, 1050-1077.
12. Davison, A.C., Smith, R.L., 1990. Models for exceedances over high thresholds. J. Roy. Statist. Soc. B 52, 393-442.
13. Dekkers, A.L.M., Einmahl, J.H., de Haan, L., 1989. A moment estimator for the index of an extreme value distribution. Ann. Statist. 17, 1833-1855.
14. Efron, B., Tibshirani, R.J., 1993. An Introduction to the Bootstrap. Chapman & Hall, London.
15. Feuerverger, A., Hall, P., 1999. Estimating a tail exponent by modelling departure from a Pareto distribution. Ann. Statist. 27, 760-781.
16. Fisher, R.A., Tippett, L.H., 1928. Limiting forms of the frequency distribution in the largest particle size and smallest number of a sample. Proc. Cam. Phil. Soc. 24, 180-190.
17. Gumbel, E.J., 1960. Statistics in Extremes. Columbia University Press, New York.
18. Hall, P., 1982. On some simple estimates of an exponent of regular variation. J. Roy. Statist. Soc. B 44, 37-42.
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., Wallis, J.R., 1987. Parameter and quantile estimation for the generalized Pareto distribution. Technometrics 29, 339-349.
21. Hosking, J.R., Wallis, J.R., Wood, E.F., 1985. Estimation of the generalized extreme-value distribution by the method of probability-weighted moments. Technometrics 27, 251-261.
22. Lawless, J.F., 1982. Statistical Models and Methods for Lifetime Data. Wiley, New York.
23. McCullagh, P., Nelder, J.A., 1992. Generalized Linear Models. Chapman and Hall, London.
24. Numerical Algorithms Group, 1993. The NAG Fortran Library Manual, Mark 16. Numerical Algorithms Group, Oxford.
25. Pickands J., III, 1975. Statistical inference using extreme order statistics. Ann. Statist. 3, 119-131.
26. Prescott, P., Walden, A.T., 1980. Maximum likelihood estimation of the parameters of the generalized extreme-value distribution. Biometrika 67, 723-724.
27. Smith, R.L., 1985. Maximum likelihood estimation in a class of nonregular cases. Biometrika 72, 67-90.
28. Smith, R.L., 1987. Estimating tails of probability distributions. Ann. Statist, 15, 1174-1207.
29. Weissman, I., 1978. Estimation of parameters and large quantiles based on the k largest observations. J. Amer. Statist. Assoc. 73, 812-815.