arXiv subjects

Nour Elhouda Guesmia

Publications and source records attributed to Nour Elhouda Guesmia.

4 recordsLinked to original sources

arXiv2026

Weighted and Truncated Tail Index Estimation under Random Censoring: A Unified Full-Range Framework

Estimation of the extreme value index under right censoring is a fundamental problem in extreme value theory, with important applications in finance, insurance, and reliability. Classical integral estimators for Pareto-type tails typically require that the asymptotic proportion of uncensored observations in the tail is larger than one half, corresponding to the weak censoring regime. This restriction excludes many practically relevant situations involving strong censoring, where the proportion of uncensored observations is smaller than or equal to one half, and reflects the absence of a uniformly valid Gaussian approximation for the associated tail empirical process. To overcome this limitation, we introduce a weighted and truncated Nelson--Aalen tail empirical process and construct a class of integral estimators indexed by a tuning parameter larger than one. This approach restores a tractable asymptotic structure over the entire censoring range, from very weak to very strong censoring. Under standard regular variation conditions, we establish a uniform Gaussian approximation and derive consistency and asymptotic normality without imposing restrictions on the censoring level. A key ingredient of the analysis is a linearization of the estimator as a functional of the underlying process. Simulation studies and real data applications demonstrate improved stability and accuracy, particularly under moderate and strong censoring. In particular, the analysis of insurance loss data, representing weak censoring, and Australian AIDS survival data, representing strong censoring, illustrates the practical relevance of the proposed methodology across contrasting censoring regimes.

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arXiv2026

Robust Tail Index Estimation under Random Censoring via Minimum Density Power Divergence

We propose a robust estimator for the tail index of Pareto-type distributions under random right-censoring, constructed within the minimum density power divergence (MDPD) framework and based on the Nelson--Aalen estimator of the cumulative hazard function. To our knowledge, this is the first application of the MDPD methodology to tail index estimation in the presence of random censoring. Under mild regularity conditions and within the weak censoring regime, the estimator is shown to be consistent and asymptotically normal. Its finite-sample performance is assessed through Monte Carlo simulations, revealing improved robustness--efficiency trade-offs compared to standard non-robust tail index estimators. Robustness is investigated under both pre-censoring and post-censoring contamination schemes. While pre-censoring contamination provides a meaningful framework for robustness assessment, post-censoring contamination directly alters the observable data and highlights the sensitivity of reconstruction-based approaches. The practical relevance of the method is illustrated using an insurance claims dataset with light censoring and fully observable extremes. An additional application to AIDS survival data is included for illustrative purposes, emphasizing the challenges encountered under stronger censoring.

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arXiv2025

Weighted Estimation of the Tail Index under Right Censorship: A Unified Approach Based on Kaplan-Meier and Nelson-Aalen Integrals

Kaplan-Meier and Nelson-Aalen integral estimators to the tail index of right-censored Pareto-type data traditionally rely on the assumption that the proportion p of upper uncensored observations exceeds one-half, corresponding to weak censoring regime. However, this condition excludes many practical settings characterized by strong censorship, where p is less than or equal to one-half. To address this bothering limitation, we propose a modification that incorporates a tuning parameter. This parameter, greater than one, assigns appropriate weights to the estimators, thereby extending the applicability of the method to the entire censoring range, where p is between zero and one. Under suitable regularity conditions, we establish the consistency and asymptotic normality of the proposed estimators. Extensive simulation studies reveal a clear improvement over existing methods in terms of bias and mean squared error, particularly in the strong censoring situation. These results highlight the significant practical and theoretical impact of our approach, offering a more flexible and accurate framework for tail index estimation under censoring. The usefulness of the method is further illustrated through its application to two real datasets: one on insurance losses (weak censoring) and the other on AIDS cases (strong censoring).

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arXiv2025

Nelson-Aalen kernel estimator to the tail index of right censored Pareto-type data

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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