Article,
Fast and Fair Simultaneous Confidence Bands for Functional Parameters
(2019)cite arxiv:1910.00131.
Abstract
Quantifying uncertainty using confidence regions is a central goal of
statistical inference. Despite this, methodologies for confidence bands in
Functional Data Analysis are underdeveloped compared to estimation and
hypothesis testing. This work represents a major leap forward in this area by
presenting a new methodology for constructing simultaneous confidence bands for
functional parameter estimates. These bands possess a number of striking
qualities: (1) they have a nearly closed-form expression, (2) they give nearly
exact coverage, (3) they have a finite sample correction, (4) they do not
require an estimate of the full covariance of the parameter estimate, and (5)
they can be constructed adaptively according to a desired criteria. One option
for choosing bands we find especially interesting is the concept of fair bands
which allows us to do fair (or equitable) inference over subintervals and could
be especially useful in longitudinal studies over long time scales. Our bands
are constructed by integrating and extending tools from Random Field Theory, an
area that has yet to overlap with Functional Data Analysis.
