Regression imputation in the functional linear model with missing values in the response

摘要

We are interested in functional linear regression when some observations of the real response are missing, while the functional covariate is completely observed. A complete case regression imputation method of missing data is presented, using functional principal component regression to estimate the functional coefficient of the model. We study the asymptotic behavior of the error when the missing data are replaced by the regression imputed value, in a 'missing at random' framework. The completed database can be used to estimate the functional coefficient of the model and to predict new values of the response. The practical behavior of the method is also studied on simulated datasets. A real dataset illustration is performed in the environmental context of air quality. (C) 2018 Elsevier B.V. All rights reserved.