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Activity Number: 284 - Statistical Learning for Dependent and Complex Data: New Directions and Innovation
Type: Invited
Date/Time: Wednesday, August 5, 2020 : 10:00 AM to 11:50 AM
Sponsor: Business and Economic Statistics Section
Abstract #309167
Title: Fast and Fair Simultaneous Confidence Bands for Functional Parameters
Author(s): Matthew Reimherr*
Companies: Penn State University
Keywords: Functional Data Analysis ; Gaussian Processes; Random Field Theory; Simultaneous Confidence Bands; Elliptical Distributions; Fairness

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. In this presentation we consider 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, but one option for choosing them 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.

Authors who are presenting talks have a * after their name.

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