Quantile Regression with Varying Coefficients

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 me...

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Bibliographic Details
Published in:The Annals of statistics 2007-02, Vol.35 (1), p.92-108
Main Author: Kim, Mi-Ok
Format: Article
Language:English
Subjects:
62G08
62G35
Approximations and expansions
Cigarette smoking
Data smoothing
Estimating techniques
Estimators
Exact sciences and technology
General topics
hypothesis test
Hypothesis testing
Knots
Linear inference, regression
Linear models
Linear regression
Mathematical analysis
Mathematical models
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical approximation
Polynomials
Probability and statistics
Quantile regression
Quantiles
Regression Analysis
Regression coefficients
regression splines
Sciences and techniques of general use
Statistics
Studies
varying-coefficient model
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Summary: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 Raoscore-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.
ISSN:0090-5364
2168-8966
DOI:10.1214/009053606000000966