Nonparametric Multivariate L1-median Regression Estimation with Functional Covariates

TL;DR

This paper introduces a nonparametric method for estimating the multivariate L1-median regression with functional covariates, establishing its consistency, asymptotic properties, and practical implementation through simulations and real data analysis.

Contribution

It proposes a new nonparametric estimator for multivariate L1-median regression with functional covariates, including theoretical properties and practical applications.

Findings

Estimator is strongly consistent and asymptotically normal.

Simulation studies demonstrate the estimator's effectiveness.

Application to real data shows advantages over marginal median regression.

Abstract

In this paper, a nonparametric estimator is proposed for estimating the L1-median for multivariate conditional distribution when the covariates take values in an infinite dimensional space. The multivariate case is more appropriate to predict the components of a vector of random variables simultaneously rather than predicting each of them separately. While estimating the conditional L1-median function using the well-known Nadarya-Waston estimator, we establish the strong consistency of this estimator as well as the asymptotic normality. We also present some simulations and provide how to built conditional con?fidence ellipsoids for the multivariate L1-median regression in practice. Some numerical study in chemiometrical real data are carried out to compare the multivariate L1-median regression with the vector of marginal median regression when the covariate X is a curve as well as X is a random vector.