  This paper presents a Bayesian sampling approach to bandwidth estimation for
the local linear estimator of the regression function in a nonparametric
regression model. In the Bayesian sampling approach, the error density is
approximated by a location-mixture density of Gaussian densities with means the
individual errors and variance a constant parameter. This mixture density has
the form of a kernel density estimator of errors and is referred to as the
kernel-form error density (c.f., Zhang et al., 2014). While Zhang et al. (2014)
use the local constant (also known as the Nadaraya- Watson) estimator to
estimate the regression function, we extend this to the local linear estimator,
which produces more accurate estimation. The proposed investigation is
motivated by the lack of data-driven methods for simultaneously choosing
bandwidths in the local linear estimator of the regression function and
kernel-form error density. Treating bandwidths as parameters, we derive an
approximate (pseudo) likelihood and a posterior. A simulation study shows that
the proposed bandwidth estimation outperforms the rule-of-thumb and
cross-validation methods under the criterion of integrated squared errors. The
proposed bandwidth estimation method is validated through a nonparametric
regression model involving firm ownership concentration, and a model involving
state-price density estimation.
