Plug-in bandwidth choice in partial linear models with autoregressive errors

Suppose that y(i) = zeta (T)(i)beta + m(t(i)) + epsilon (i), i = 1, . . . , n, where the (p x 1)-vector beta and the function in are unknown, and the errors epsilon (i) follow a stationary autoregressive process of known order k greater than or equal to 1. The problem of bandwidth selection for an estimator of beta is addressed here. We obtain second-order approximations to the moments of the truncated standardized estimator, which are used to define an optimal bandwidth. Then, we propose to use a plug-in methodology in order to estimate this bandwidth through preliminary estimates of the unknown quantities. Asymptotic normality for our estimator is also established. The obtained results are a generalization of those obtained by Linton (1995) assuming independence between the errors, and the same orders as in the independent case are obtained. (C) 2002 Elsevier Science B.V. All rights reserved.