Estimation and Variable Selection under the Function-on-scalar Linear Model with Covariate Measurement Error

Abstract

Function-on-scalar linear regression has been widely used to model the relationship between a functional response and multiple scalar covariates. Its utility is, however, challenged by the presence of measurement error, a ubiquitous feature in applications. Naively applying usual function-on-scalar linear regression to error-contaminated data often yields biased inference results. Further, estimation of the model parameters is complicated by the presence of inactive variables, especially when handling data with a large dimension. Building parsimonious and interpretable function-on-scalar linear regression models is in urgent demand to handle error-contaminated functional data. In this paper, we study this important problem and investigate the measurement error effects. We propose a debiased loss function, combined with a sparsity-inducing penalty function, to