Residual estimators
(2001) Journal of Statistical Planning and Inference — Vol. 98, n° 1/2, p. 15-27 (2001)
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- Authors
- Abstract
- We define a new class of estimators of the positive extreme value index γ, called residual estimators, by replacing the logarithm in the definition of the Hill estimator by an arbitrary function f. If the sample comes from a distribution in the max-domain of attraction D(Φ1/γ), the residual estimator thus obtained converges weakly to a function of γ determined by f. Under certain natural conditions, the estimator is asymptotically normal. Among all residual estimators, the Hill estimator has the smallest asymptotic variance.
- Affiliations
Katholieke Universiteit Leuven Departement Wiskunde
Citations
Segers, J. (2001). Residual estimators. Journal of Statistical Planning and Inference, 98(1/2), 15-27. https://doi.org/10.1016/S0378-3758(00)00321-9 (Original work published 2001)