Estimation, imputation and prediction for the functional linear model with scalar response with responses missing at random Articles uri icon

publication date

  • March 2019

start page

  • 91

end page

  • 103

volume

  • 131

international standard serial number (ISSN)

  • 0167-9473

electronic international standard serial number (EISSN)

  • 1872-7352

abstract

  • Two different methods for estimation, imputation and prediction for the functional linear model with scalar response when some of the responses are missing at random (MAR) are developed. The simplified method consists in estimating the model parameters using only the pairs of predictors and responses observed completely. In addition the imputed method consists in estimating the model parameters using both the pairs of predictors and responses observed completely and the pairs of predictors and responses imputed with the parameters estimated with the simplified method. The two methodologies are compared in an extensive simulation study and the analysis of two real data examples. The comparison provides evidence that the imputed method might have better performance than the simplified method if the numbers of functional principal components used in the former strategy are selected appropriately. (C) 2018 Elsevier B.V. All rights reserved.

keywords

  • functional linear model; imputation of missing responses; mean square error of estimation; mean square error of prediction; missing at random; scalar response; regression; convergence; rates