Functional linear model with partially observed covariate and missing values in the response

Abstract

Dealing with missing values is an important issue in data observation or data recording process. In this paper, 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 behaviour of the prediction error when missing data are replaced by the imputed values in the original dataset. The practical behaviour of the method is also studied on simulated data and a real dataset.

Keywords:

• Functional linear model
• functional principal components
• missing data
• missing at random
• missing completely at random
• regression imputation

AMS Subject Classifications:

• 62G20
• 62J05
• 62F12
• 62P99

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 https://www.agora-energiewende.de/en/service/recent-electricity-data/chart/power_generation/15.03.2012/14.03.2013/

2 https://automeris.io/WebPlotDigitizer/