M. Alcalde, M. Lafuente, F. J. López, G. Sanz
Let {X_n} be a sequence of i.i.d. random variables with a nonnegative continuous cdf F. The distribution F is Pareto-like if there exists γ > 0 such that, for all t > 0, (1 - F(tx)) / (1 - F(x)) → 1/t^γ as x → ∞. The parameter γ is known as the tail index. Since Hill's estimator was introduced in 1975, several modifications have appeared in the literature, all based on order statistics. We propose a nonparametric estimator for γ based on geometric δ-records instead, making it more suitable for inverse sampling, particularly in destructive testing, common in reliability analysis. Given a sequence as above and 0 < δ < 1, X_i is a geometric δ-record if X_i > δ max{X_1,...,X_{i-1}}. The proposed estimator outperforms Hill's in terms of the MSE-to-cost ratio for the Pareto distribution. Additionally, we prove its strong consistency and asymptotic normality for this distribution and explore their extension to the Pareto-like case.
Keywords: Tail index, Pareto-like distributions, records, δ-records, near-records, nonparametric statistical inference
Scheduled
Stochastic processes and their applications I
June 13, 2025 11:00 AM
Auditorio 2. Leandre Cristòfol