Plug-in bandwidth choice for estimation of nonparametric part in partial linear regression models with strong mixing errors

Consider a regression model where the regression function is the sum of a linear and a nonparametric component. Assuming that the errors of the model follow a stationary strong mixing process with mean zero, the problem of bandwidth selection for a kernel estimator of the nonparametric component is addressed here. We obtain an asymptotic expression for an optimal band-width and we propose to use a plug-in methodology in order to estimate this bandwidth through preliminary estimates of the unknown quantities. Asymptotic optimality for the plug-in bandwidth is established.