A generalized correlated Cp criterion for derivative estimation with dependent errors

Abstract

In practice, it is common that errors are correlated for the nonparametric regression model. Although many methods have been developed for addressing correlated errors for tuning parameter selection to recover the mean response function, few studies have been proposed to select tuning parameters for derivative estimation. In this paper, a generalized correlated Cp (GCCp) criterion is proposed to choose a tuning parameter for derivative estimation in the presence of correlated errors. It can be applied for any nonparametric estimation linear in responses, including kernel regression, local regression, smoothing spline, etc. The GCCp criterion is justified both theoretically and empirically via simulation studies. Finally, an air quality index data example in Changsha city is provided to illustrate the application of the proposed criterion.