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.
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Acknowledgement
Sincere thanks to Hira L. Koul, an inspiration to us and to others who have guided, challenged, and inspired us. I. Van Keilegom acknowledges financial support from the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007-2013)/ERC Grant agreement No. 203650, from IAP research network P7/06 of the Belgian Government (Belgian Science Policy), and from the contract ‘Projet d’Actions de Recherche Concertées’ (ARC) 11/16-039 of the ‘Communauté française de Belgique’, granted by the ‘Académie universitaire Louvain’. The authors would also like to thank two referees for their helpful comments.
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Müller, U., Van Keilegom, I. (2014). Efficient Quantile Regression with Auxiliary Information. In: Lahiri, S., Schick, A., SenGupta, A., Sriram, T. (eds) Contemporary Developments in Statistical Theory. Springer Proceedings in Mathematics & Statistics, vol 68. Springer, Cham. https://doi.org/10.1007/978-3-319-02651-0_23
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DOI: https://doi.org/10.1007/978-3-319-02651-0_23
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