Improved double kernel local linear quantile regression

As sample quantiles can be obtained as maximum likelihood estimates of location parameters in suitable asymmetric Laplace distributions, so kernel estimates of quantiles can be obtained as maximum likelihood estimates of location parameters in a general class of distributions with simple exponential tails. In this paper, this observation is applied to kernel quantile regression. In so doing, a new double kernel local linear quantile regression estimator is obtained which proves to be consistently superior in performance to the earlier double kernel local linear quantile regression estimator proposed by the authors. It is also particularly straightforward to compute. An alternative method of selection for one of the two bandwidths involved also arises naturally but proves not to be so consistently successful.