N. Mohammadi, V. Panaretos, L. Santoro
FDA covers a central role in studying different inference problems, allowing to consider functional datasets on complex domains. For discrete observations, this approach basically imposes some smoothness conditions on the sample paths and/or their covariance function to apply approximating methods. However, the usual regularity assumptions limit the appropriateness of FDA in many common settings, most notably SDE. We introduce a modification of existing methods, dubbed the reflected triangle estimator and make inferences about the global behavior of the diffusion processes. We show that this allows for the FDA of processes with nowhere differentiable sample paths, even when these are discretely and noisily observed. We then relate the global behavior of the processes to their local behavior by means of a novel PDE. We establish almost sure uniform asymptotic convergence rates of the proposed estimators as the number of observed curves grows to infinity.
Keywords: Brownian motion, FDA, Ito diffusion process, Local polynomial regression, reflected triangle, Sparse sampling, SDE Local linear smoothing
Scheduled
GT06 Functional Data Analysis IV. Functional Time Series
June 9, 2022 10:10 AM
Grade Hall
