Local polynomial regression with correlated errors in random design and unknown correlation structure

Automated or data-driven bandwidth selection methods tend to break down in the presence of correlated errors. While this problem has previously been studied in the fixed design setting for kernel regression, the results were applicable only when there is knowledge about the correlation structure. This article generalizes these results to the random design setting and addresses the problem in situations where no prior knowledge about the correlation structure is available. We establish the asymptotic optimality of our proposed bandwidth selection criterion based on kernels K satisfying K(0) = 0.