This repository contains presentation slides for a joint project with Valenti Patilea.
Abstract: One drawback with classical smoothing methods (kernels, splines, wavelets etc.) is their reliance on assuming the degree of smoothness (and thereby assuming continuous differentiability up to some order) for the underlying object being estimated. However, the underlying object may in fact be irregular (i.e., non-smooth and even perhaps nowhere differentiable) and, as well, the (ir)regularity of the underlying function may vary across its support. Elaborate adaptive methods for curve estimation have been proposed, however, their intrinsic complexity presents a formidable and perhaps even insurmountable barrier to their widespread adoption by practitioners. We contribute to the functional data literature by providing a pointwise MSE-optimal, data-driven, iterative plug-in estimator of “local regularity” and a computationally attractive, recursive, online updating method. In so doing we are able to separate measurement error “noise” from “irregularity” thanks to “replication”, a hallmark of functional data. Our results open the door for the construction of minimax optimal rates, “honest” confidence intervals, and the like, for various quantities of interest.
The slides can be accessed via https://jeffreyracine.github.io/Braga
The GitHub repository for this project is https://github.com/JeffreyRacine/Braga (you are here!)
To generate the slides, a) click the CODE icon in the GitHub repository, b) click on Download ZIP, c) unzip the download, d) open index.qmd in RStudio, e) click Render in RStudio (you may have to install a few packages - click install if presented with the option), f) be patient, the code can take some time to run and complete.