Linear Regression Using Principal Components from General Hilbert-Space-Valued Covariates

Xinyi Li; Margaret Hoch; Michael R. Kosorok

Paper

Linear Regression Using Principal Components from General Hilbert-Space-Valued Covariates

Abstract

We present a new method of linear regression based on principal components using Hilbert-space-valued covariates. We develop a computationally efficient approach to estimation and derive asymptotic theory for the regression parameter estimates under mild assumptions. We demonstrate the approach in simulation studies as well as in data analysis using two-dimensional brain images as predictors.