Statistical Modelling 7 (2007), 377376
Improved double kernel local linear quantile regression
M C Jones
Department of Statistics,
The Open University,
UK
KemingYu
Department of Mathematical Sciences,
Brunel University,
Uxbridge, UB8 3PH
UK
eMail:
keming.yu@brunel.ac.uk
Abstract:
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 doing so, 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 straightforward
to compute and more readily affords a first derivative estimate. An
alternative method of selection for one of the two bandwidths involved
also arises naturally but proves not to be so consistently successful.
Keywords:
asymmetric Laplace distribution; bandwidth selection;
exponential tails; maximum likelihood
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