Nonparametric estimation of the derivative of the regression function: application to sea shores water quality

TL;DR

This paper introduces an efficient nonparametric method for estimating the derivative of a regression function, with applications to water quality assessment at sea shores, supported by theoretical convergence results and real data illustrations.

Contribution

It proposes a novel recursive Nadaraya-Watson based estimator for derivatives, with proven convergence and normality, and demonstrates its effectiveness on environmental data.

Findings

Estimator converges almost surely

Estimator is asymptotically normal

Effective on simulated and real data

Abstract

This paper is devoted to the nonparametric estimation of the derivative of the regression function in a nonparametric regression model. We implement a very efficient and easy to handle statistical procedure based on the derivative of the recursive Nadaraya-Watson estimator. We establish the almost sure convergence as well as the asymptotic normality for our estimates. We also illustrate our nonparametric estimation procedure on simulated and real life data associated with sea shores water quality and valvometry.