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

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.