Kernel regression for estimating regression function and its derivatives with unknown error correlations

In practice, it is common that errors are correlated in the nonparametric regression model. Although many methods have been developed for addressing correlated errors, most of them rely on accurate estimation of correlation structure. A couple of methods have been proposed to avoid prior information of correlation structure to estimate regression function. However, the derivative estimation is also crucial to some practical applications. In this article, a bandwidth selection procedure is proposed for estimating both mean response and derivatives via kernel regression when correlated errors present. Both empirical support and theoretical justification are provided for the estimation procedure. Finally, we describe a Beijing temperature data example to illustrate the application of the proposed method.