The reproducing kernel Hilbert space approach in nonparametric regression problems with correlated observations

Abstract

In this paper we investigate the problem of estimating the regression function in models with correlated observations. The data is obtained from several experimental units each of them forms a time series. We propose a new estimator based on the inverse of the autocovariance matrix of the observations, assumed known and invertible. Using the properties of the Reproducing Kernel Hilbert spaces, we give the asymptotic expressions of its bias and its variance. In addition, we give a theoretical comparison, by calculating the IMSE, between this new estimator and the classical one proposed by Gasser and Muller. Finally, we conduct a simulation study to investigate the performance of the proposed estimator and to compare it to the Gasser and Muller's estimator in a finite sample set.