Multiple imputation in the functional linear model with partially observed covariate and missing values in the response

Abstract

. Missing data problems are common and difficult to handle in data analysis. Ad hoc methods, such as simply removing cases with missing values, can lead to invalid analysis results. In this article, we consider a functional linear regression model with partially observed covariate and missing values in the response. We use a reconstruction operator that aims at recovering the missing parts of the explanatory curves, then we are interested in regression imputation method of missing data on the response variable, using functional principal component regression to estimate the functional coefficient of the model. We study the asymptotic behavior of the prediction error when missing values in an original dataset are imputed by multiple sets of plausible values. The method behavior is also evaluated in practice.