A1172
Title: Penalized spline M-estimators for discretely sampled functional data: Existence and asymptotics
Authors: Ioannis Kalogridis - University of Glasgow (United Kingdom) [presenting]
Abstract: Location estimation is a central problem in functional data analysis. Penalized spline estimators of location for discretely sampled functional data are investigated under a broad class of convex loss functions. The framework generalizes and extends previously derived results for non-robust estimators to a broad penalized M-estimation framework. The analysis is built on two general-purpose non-asymptotic theoretical tools: (i) a non-asymptotic existence result for penalized spline estimators under minimal design conditions, and (ii) a localization lemma that captures both stochastic variability and approximation error. Under mild assumptions, optimal convergence rates are established and the small and large knot regimes are identified, along with the critical breakpoint known from penalized spline theory in nonparametric regression. The results imply that parametric rates are attainable even with discretely sampled data, and numerical experiments demonstrate that the estimators match or exceed the robustness of competing estimators while being considerably more computationally attractive.
