Inference for Functional Data
Conducting inference, i.e. performing hypothesis testing, on functional data is a challenge due to the dimensionality of the problem. My previous work in this area has been in the Bayesian context where I developed the Simultaneous Band Scores or SimBaS procedure. More recently, I have several on-going projects using non-Bayesian (or at least not fully Bayesian) methods.
Doubly Ranked Tests
The Doubly Ranked Test or DRT, is a novel nonparametric framework for analyzing groups of functional curves. The approach first ranks the data at each time point (or location) and then summarizes the ranks across time (or location). The subject-specific rank summaries are then analyzed using well-known nonparametric tests.
One of my more recent projects, the first manuscript on this topic has been accepted at Statistical Science; a pre-print is available on arXiv. Code is available on CRAN using the R package runDRT.
Testing Variational Semiparametric and Functional Effects
Inferential methods for variational Bayesian methods are limited and can have issues with variance estimation. In this project, I examine the operating characteristics of a Frequentist test for smoothed curves in a variational context, specifically for testing components in additive scalar-on-function regression models including semiparametric and functional effects. The model can accommodate both Gaussian and Binary response.
A pre-print of this is available on arXiv.
SimBaS
The simultaneous band scores, or SimBaS, procedure leverages the posterior sample from a Bayesian functional model to construct simultaneous or joint credible intervals. The SimBaS Score is then the smallest alpha value at which the interval first excludes zero.
This method can be implemented in any Bayesian functional regression setting. In my work, I have used it in function-on-function, historical, and functional outcome regression settings.
Additional Work
My on-going work in this area includes a comparison of Bayesian functional intervals, extending the doubly ranked tests to other settings, two stage tests for functional data, and two sample tests for variational effects. Check back for updates on these projects.