The stochastic approximation method for semi-recursive multivariate kernel-type regression estimation

Abstract

In this research paper, we elaborate an extension of the semi-recursive kernel-type regression function estimator. We investigate the asymptotic properties of this estimator and compare them with non-recursive Nadaraya Watson regression estimator. From this perspective, we first calculate the bias and the variance of the proposed estimator which strongly depend on the choice of three parameters, namely the stepsizes (βn) and (γn) as well as the bandwidth (hn) chosen using one of the best methods of bandwidth selection, the bootstrap approach compared to the plug-in method. An appropriate choice of those parameters yields that, under some conditions, the MSE (Mean Squared Error) of the proposed estimator can be smaller than that of Nadaraya Watson's estimator. We corroborate our theoretical results through simulations studies and by considering two real dataset applications, the French Hospital Data of COVID-19 epidemic as well as the Plasmodium Falciparum Parasite Load (PL).