Scalar-on-Function Regression with Measurement Error in the Functional Regressors

• Activity Number: 638
• Type: Topic Contributed
• Date/Time: Thursday, August 7, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Xiaochen Cai*+ and R. Todd Ogden
• Companies: Columbia University and Columbia University
• Keywords: Measurement error ; Scalar-on-function regression ; Simulation-extrapolation ; Pre-smoothing

Abstract

We consider the problem of functional linear regression where the responses are scalar and the regressors are functions. Most existing methods implicitly assume that the functional covariates are observed exactly, but in practice, they are often contaminated by some measurement error. Our goal, therefore, is to deal with the problem of the scalar-on-function regression when the regressor functions are observed with error. In this presentation, we describe a simulation-extrapolation method to correct for the attenuation of estimated coefficient functions caused by the error. The method first estimates the error variance, establishes the relationship between a sequence of added error variance and the corresponding estimates of coefficient functions, and then extrapolates to the zero-error. We describe three methods to extrapolate the sequence of estimated coefficient functions. In a simulation study, we compare the performance of the simulation-extrapolation method with two pre-smoothing methods based on smoothing splines and functional principal component analysis.