Supplement to 'Estimation in Functional Regression for General Exponential Families'

Abstract

In this supplemental article, we introduce some useful results in spectral theory and perturbation theory. Some of the results are well-established. We briefly review them for the purpose of easy reference. We derive a novel bound for the perturbation of eigenprojections, which plays a key role in the slope function estimation problem.

Keywords: Approximation of Compact Operators, Assouad’s Lemma, Exponential Families, Functional Estimation, Mini Max Rates of Convergence

JEL Classification: C1, C2, C4, C5