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Published in:
2014 | OriginalPaper | Chapter
23. Efficient Quantile Regression with Auxiliary Information
Authors : Ursula U. Müller, Ingrid Van Keilegom
Published in: Contemporary Developments in Statistical Theory
Publisher: Springer International Publishing
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Abstract
We discuss efficient estimation in quantile regression models where the quantile regression function is modeled parametrically. In addition, we assume that auxiliary information is available in the form of a conditional constraint. This is, for example, the case if the mean regression function or the variance function can be modeled parametrically, e.g., by a line or a polynomial. In this chapter, we describe efficient estimators of parameters of the quantile regression function for general conditional constraints and for examples of more specific constraints. We do this more generally for a model with responses missing at random, for which an efficient estimator is provided by a complete case statistic. This covers the usual model as a special case. We discuss several examples and illustrate the results with simulations.