6:00 PM Seminar Begins
7:30 PM Reception
Hybrid Event:
Fordham University
McNally Amphitheater
140 West 62nd Street
New York, NY 10023
Free Registration!
For Virtual Attendees: Please select virtual instead of member type upon registration.
Abstract:
Functional Data Analysis (FDA) plays an undeniably central role in studying various statistical inference problems, allowing consideration of functional datasets on potentially complex domains, with trajectories observed discretely or continuously. Regarding discrete observations, this approach essentially imposes some smoothness conditions on the sample paths and/or their covariance function to apply well-developed approximating methods. However, the usual regularity assumptions seriously limit the applicability of FDA in many commonly encountered settings, most notably stochastic differential equations (SDEs). In this talk, we introduce a careful modification of existing methods, dubbed the "reflected triangle estimator," and make inferences about the global behavior of 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, including under irregular and sparse designs. We then proceed to relate the global behavior of the processes to their local behavior by means of an apparently novel PDE. We establish almost sure uniform asymptotic convergence rates of the proposed estimators as the number of observed curves grows to infinity. Our rates are non-asymptotic in the number of measurements per path, explicitly reflecting how different sampling frequencies might affect the speed of convergence.
This talk builds on two papers: Functional Data Analysis with Rough Sample Paths? (Mohammadi and Panaretos, 2024) and Nonparametric Estimation for SDEs with Sparsely Sampled Paths: An FDA Perspective (Mohammadi et al., 2024).
Bio:
Dr. Neda Mohammadi is a tenure-track assistant professor in the Department of Mathematics and Statistics at North Carolina A&T State University (NCAT), USA. Her research focuses on Functional Data Analysis (FDA), Stochastic Processes, and Time Series Analysis, particularly in the spectral domain. She works at the intersection of FDA, frequency domain time series analysis, and statistical inference for (Itô) diffusion-modeled random processes. More recently, she has been developing deep learning methods for FDA in the spectral domain. Prior to her current position, Dr. Mohammadi held postdoctoral fellowships at Colorado State University (CSU), USA, and École Polytechnique Fédérale de Lausanne (EPFL), Switzerland. She earned her PhD in Statistics from Isfahan University of Technology (IUT), Iran, where her research focused on periodically correlated functional time series.
