ABSTRACT
We describe in this chapter a class of two-step local smoothing methods for the estimation of the coefficient curves β (t) in the time-varying coefficient model (7.1). This class of estimators is based on the simple idea that the coefficient curves β (t) can be first estimated by the least squares method at a sequence of isolated time points, and then these isolated estimates can be treated as pseudo-observations and smoothed over to produce the final smoothed estimator of β (t). Compared with the one-step local smoothing methods in Chapter 7, this class of methods have two major advantages. First, the two-step smoothing methods of this chapter can naturally incorporate different bandwidths for different components of β (t), which provides some additional flexibility for adjusting the possibly different smoothing needs in β (t). Second, since the two-step smoothing methods only depend on the existing estimation methods, they are computationally simple, and their bandwidths can be easily selected by modifying the cross-validation procedures with the classical cross-sectional i.i.d. data. The idea of two-step smoothing can be generalized to other structured nonparametric models constructed from some local parametric or semiparametric models when t is fixed, such as the timevarying transformation models of Chapters 13 and 14, in which the two-step estimation approach is the only available option in the literature.
