<p>It is well known that classical bandwidth selection methods break down in the presence of correlation Often, semivariogram models are used to estimate the correlation function, or the correlation structure is assumed to be known. The estimated or known correlation function is then incorporated into the bandwidth selection criterion to cope with this type of error. In the case of (nonparametric) regression estimation, one is usually not interested in the correlation function itself but rather in the conditional mean function. This article proposes a multivariate nonparametric method to handle correlated errors and particularly focuses on the problem when no prior knowledge about the correlation structure is available and neither does the correlation function need to be estimated. We establish the asymptotic optimality of our proposed bandwidth selection criterion based on a special type of kernel. Finally, we show the asymptotic normality of the multivariate local linear regression estimator for dependent errors based on stochastic bandwidth matrices.</p>