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Improved double kernel local linear quantile regression

M C Jones is at Department of Statistics, The Open University, UK

Keming Yu

KemingYu is at Department of Mathematical Sciences, Brunel University, UK. E-mail: keming.yu{at}brunel.ac.uk

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.

Key Words: asymmetric Laplace distribution • bandwidth selection • exponential tails • maximum likelihood

Statistical Modelling, Vol. 7, No. 4, 377-389 (2007)
DOI: 10.1177/1471082X0700700407


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