Pareto approximation of the tail by local exponential modeling
- Grama, Ion G.
- Spokoiny, Vladimir
2010 Mathematics Subject Classification
- 62G32 62G05
- Hill estimator, tail index, adaptive choice, model Hill estimator, extreme values
We give a new adaptive method for selecting the number of upper order statistics used in the estimation of the tail of a distribution function. Our approach is based on approximation by an exponential model. The selection procedure consists in consecutive testing for the hypothesis of homogeneity of the estimated parameter against the change-point alternative. The selected number of upper order statistics corresponds to the first detected change-point. Our main results are non-asymptotic and state optimality of the proposed method in the "oracle" sense.