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 record-2 Christophe Crambes et al.ing 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 coe cient 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.

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

“…Other recent works explore this context but in a nonparametric setting (Wang et al, 2019;Rachdi et al, 2020) or in a functional partial linear regression setting (Ling et al, 2019;Zhou and Peng, 2020) or while the response is not missing at random (Li et al, 2018). More recently, Crambes et al (2022) are interested in a more general case of missing data in functional linear regression: when the covariate is partially observed and when the response is affected by missing data. Following this latter paper (Crambes et al, 2022, Subsection 2.1 and Subsection 2.2), p η n can be calculated using the curve reconstruction method of Kneip and Liebl (2020, Section 2).…”

“…More recently, Crambes et al (2022) are interested in a more general case of missing data in functional linear regression: when the covariate is partially observed and when the response is affected by missing data. Following this latter paper (Crambes et al, 2022, Subsection 2.1 and Subsection 2.2), p η n can be calculated using the curve reconstruction method of Kneip and Liebl (2020, Section 2). We give here some essential elements for our work: we consider a reconstruction problem relating the missing part of the curves to the observed part, writing…”

“…In this section, we follow the same steps as in Crambes et al (2022). Using the exponent notation "obs" to make reference to the units for which the response is observed, we define the covariance operator with the reconstructed curves (2.1) as follows…”

“…An asymptotic behavior of the prediction error is given in Crambes et al (2022) when the missing parts of the covariate are reconstructed and the missing values on the response are imputed by deterministic regression imputation. In the next section, we will study the convergence rate of this prediction error with multiple regression imputation.…”

A Comprehensive Bibliometric Analysis of Missing Value Imputation

“…While large datasets may allow for value disregarding, removing records with missing values in smaller datasets can lead to inaccurate classification or predictions using DM algorithms [1]. Addressing missing values during data observation or recording is a significant concern [11], [12].…”