Colloquium Speaker:
Dr. Lahcen Douge, Ph.D.
Cadi Ayaad University, Marrakech, Morocco
Title: Recent Advances in nonparametric estimation under weak dependence
Abstract: In this talk, we present recent advances in nonparametric estimation for dependent data, focusing on Bernstein polynomial estimators for quantile, distribution, and density functions under weak dependence. We first examine the asymptotic properties of Bernstein estimators for distribution and density functions, establishing their strong consistency and asymptotic normality under general regularity conditions. Next, we develop Bahadur-type representations for quantile estimators, demonstrating how the rate of approximation depends on the decay of dependence coefficients. When these coefficients decay rapidly, the optimal convergence rates known in the independent case are recovered. Furthermore, we derive a Berry–Esseen bound for the sample quantiles.
Finally, Monte Carlo simulations based on some weakly dependent models—which are not necessarily mixing—illustrate that Bernstein estimators can outperform both empirical estimators and classical kernel-based methods.
Day & Time: Tuesday, May 6, 2025, at 3:00pm
Location: Lambton Tower, Room 9-118
Counts toward seminar attendance for MSc and PhD students in Math & Stats.