Partially function linear error-in-response models with validation data

Abstract

This paper considers partial function linear models of the form Y = ∫ X(t)β(t)dt + g(T) with Y measured with error. The authors propose an estimation procedure when the basis functions are data driven, such as with functional principal components. Estimators of β(t) and g(t) with the primary data and validation data are presented and some asymptotic results are given. Finite sample properties are investigated through some simulation study and a real data application.