|
Abstract:
|
This work is concerned with developing, understanding, and visualizing confidence regions for functional parameters. We propose two general geometric forms of confidence regions - hyper-ellipsoids and hyper-rectangles - and show how those regions can be tailored to achieve proper coverage probability. While these regions, based on a functional principal component(FPC) coordinate system, achieve proper coverage when using population level FPCs, we demonstrate that they, and many natural regions, have zero coverage when working with the empirical FPCs. We therefore propose a new paradigm for evaluating confidence regions by showing that the distance between an estimated region and the desired region tends to zero faster than the regions are shrinking to a point. We call this phenomena ghosting and refer to the empirical regions as ghost regions. To illustrate these methods we present an extensive simulation study and an application to fractional anisotropy.
|
