Quantile regression with varying coefficients

Details Quantile regression with varying coefficients Quantile regression with varying coefficients

2007-08-03

arxiv.org/abs/0708.0471v1

Annals of Statistics 2007, Vol. 35, No. 1, 92-108

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/009053606000000966 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

10.1214/009053606000000966

Quantile regression provides a framework for modeling statistical quantities of interest other than the conditional mean. The regression methodology is well developed for linear models, but less so for nonparametric models. We consider conditional quantiles with varying coefficients and propose a methodology for their estimation and assessment using polynomial splines. The proposed estimators are easy to compute via standard quantile regression algorithms and a stepwise knot selection algorithm. The proposed Rao-score-type test that assesses the model against a linear model is also easy to implement. We provide asymptotic results on the convergence of the estimators and the null distribution of the test statistic. Empirical results are also provided, including an application of the methodology to forced expiratory volume (FEV) data.

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