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

Christophe Crambes (1) , Chayma Daayeb (1, 2) , Ali Gannoun (1) , Yousri Henchiri (2, 3)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier
2 UTM - Université de Tunis El Manar
3 Université de la Manouba, ISAMM, Tunisie.

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 behavior of the prediction error when missing data are replaced by the imputed values in the original dataset. The practical behavior of the method is also studied on simulated data and a real dataset.

Mots clés: Functional linear model; Missing data; Functional Principal Components; Missing At Random; Missing Completely At Random; Regression imputation

Domaines: Statistiques [math.ST]; Probabilités [math.PR]

Christophe Crambes, Chayma Daayeb, Ali Gannoun, Yousri Henchiri. Functional linear model with partially observed covariate and missing values in the response.. 2021. ⟨hal-03083293v2⟩