Séminaire Jeunes chercheurs (Nassim Bourarach, jeudi 15 janvier 2026)

La prochaine séance du séminaire Jeunes chercheurs du CEREMADE aura lieu le jeudi 15 janvier 2026 à 17h en salle A707. Nous aurons le plaisir d'écouter Nassim BOURARACH (CEREMADE), qui nous parlera de

Estimating Principal Modes of Random Functions from Noisy Samples of Observations on a Common Grid : Identifiability and Minimax Estimation.

Abstract
One can study random curves either from a stochastic-process perspective (specifying a probabilistic model for paths) or from a Functional Data Analysis (FDA) perspective (treating each realization as a function and focusing on dimension reduction and inference in function spaces). This talk adopts the FDA viewpoint through functional principal component analysis (FPCA), but in a setting that is natural for stochastic processes: we observe independent trajectories only at finitely many common time points and with additive noise. I will explain what can and cannot be estimated in a minimax sense, why kernel smoothness alone does not ensure identifiable eigenfunctions, and how a weighted spectral gap condition restores minimax-consistent estimation. We then obtain sharp nonasymptotic lower bounds that separate sampling and discretization effects and exhibit phase transitions, and we present a computable wavelet projection estimator that achieves matching upper bounds in theory.