Nelson-Aalen kernel estimator to the tail index of right censored Pareto-type data
By: Nour Elhouda Guesmia, Abdelhakim Necir, Djamel Meraghni
Potential Business Impact:
Estimates how often big losses happen in insurance.
On the basis of Nelson-Aalen product-limit estimator of a randomly censored distribution function, we introduce a kernel estimator to the tail index of right-censored Pareto-like data. Under some regularity assumptions, the consistency and asymptotic normality of the proposed estimator are established. A small simulation study shows that the proposed estimator performs much better, in terms of bias and stability, than the existing ones with, a slight increase in the mean squared error. The results are applied to insurance loss data to illustrate the practical effectiveness of our estimator.
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