JTJalal Taher
Jalal Taher
*This is an algorithmically generated author record based on publicly available information.
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The organizations/institutes from the scholar's latest article
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Jalal Taher has a total of 2 co-authors. Here are the top co-authors by number of shared publications:
- Céline Duval
Laboratoire de Probabilités, Statistique et Modélisation
2 shared publications - Ester Mariucci
Université Paris-Saclay, UVSQ, CNRS, Laboratoire de Mathématiques de Versailles, Versailles, France
2 shared publications
Latest Publications
- 6 September 2025
- Published by Springer Nature in Statistical Inference for Stochastic Processes
- Vol. 28 (3) , 1-26
Nonparametric density estimation for the small jumps of Lévy processes
- 6 September 2025
- Published by Springer Nature in Statistical Inference for Stochastic Processes
- Vol. 28 (3) , 1-26
Nonparametric density estimation for the small jumps of Lévy processes
- Open Access
Adaptive minimax estimation for discretely observed Lévy processes
In this paper, we study the nonparametric estimation of the density $f_Δ$ of an increment of a Lévy process $X$ based on $n$ observations with a sampling rate $Δ$. The class of Lévy processes considered is broad, including both processes with a Gaussian component and pure jump processes. A key focus is on processes where $f_Δ$ is smooth for all $Δ$. We introduce a spectral estimator of $f_Δ$ and derive both upper and lower bounds, showing that the estimator is minimax optimal in both low- and high-frequency regimes. Our results differ from existing work by offering weaker, easily verifiable assumptions and providing non-asymptotic results that explicitly depend on $Δ$. In low-frequency settings, we recover parametric convergence rates, while in high-frequency settings, we identify two regimes based on whether the Gaussian or jump components dominate. The rates of convergence are closely tied to the jump activity, with continuity between the Gaussian case and more general jump processes. Additionally, we propose a fully data-driven estimator with proven simplicity and rapid implementation, supported by numerical experiments.Open AccessAdaptive minimax estimation for discretely observed Lévy processes
In this paper, we study the nonparametric estimation of the density $f_Δ$ of an increment of a Lévy process $X$ based on $n$ observations with a sampling rate $Δ$. The class of Lévy processes considered is broad, including both processes with a Gaussian component and pure jump processes. A key focus is on processes where $f_Δ$ is smooth for all $Δ$. We introduce a spectral estimator of $f_Δ$ and derive both upper and lower bounds, showing that the estimator is minimax optimal in both low- and high-frequency regimes. Our results differ from existing work by offering weaker, easily verifiable assumptions and providing non-asymptotic results that explicitly depend on $Δ$. In low-frequency settings, we recover parametric convergence rates, while in high-frequency settings, we identify two regimes based on whether the Gaussian or jump components dominate. The rates of convergence are closely tied to the jump activity, with continuity between the Gaussian case and more general jump processes. Additionally, we propose a fully data-driven estimator with proven simplicity and rapid implementation, supported by numerical experiments.