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Econometric Theory, 32, 2016, 686713. doi:10.1017/S0266466615000031
WALTER OBERHOFER University of Regensburg
HARRY HAUPT University of Passau
This paper studies the asymptotic properties of the nonlinear quantile regression model under general assumptions on the error process, which is allowed to be heterogeneous and mixing. We derive the consistency and asymptotic normality of regression quantiles under mild assumptions. First-order asymptotic theory is completed by a discussion of consistent covariance estimation.
1. INTRODUCTION
The concept of quantile regression introduced in the seminal paper of Koenker and Bassett (1978), has become a widely used and accepted technique in many areas of theoretical and applied econometrics. The rst monograph on this topic has been published by Koenker (2005), covering a wide scope of well established foundations and (even a twilight zone of) actual research frontiers. In addition, many of the numerous new concepts in this fast evolving eld have been reviewed and summarized in survey articles (see inter alia Buchinsky, 1998; Yu, Lu, and Stander, 2003) and econometric textbooks (e.g., Peracchi, 2001; Wooldridge, 2010). In contrast to the more methodological literature, there are also important, nontechnical attempts to bring the key concepts and especially the applicability of quantile estimation to a wider audience outside the statistical profession (e.g., Koenker and Hallock, 2001).
This paper deals with quantile regressions where the dependent variable y and covariates x1,..., xK satisfy a nonlinear model with additive errors. Let ( ,F, P)
Our heartfelt thanks to Matei Demetrescu, Bernd Fitzenberger, Keith Knight, Rolf Tschernig, and especially Roger Koenker for encouraging discussions on earlier drafts of the paper. The second author gratefully acknowledges nancial support of the International Centre for Mathematical Sciences (ICMS). Finally we thank three anonymous referees and the associate editor Oliver Linton for helpful comments and suggestions. Of course all remaining errors are ours. Address correspondence to Harry Haupt, Department of Statistics, University of Passau, 94030 Passau, Germany; e-mail: [email protected].
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Cambridge University Press 2015
ASYMPTOTIC THEORY FOR NONLINEAR QUANTILE REGRESSION UNDER WEAK
DEPENDENCE
NONLINEAR QUANTILE REGRESSION 687
be a complete probability space and let {yt}tN be an F-measurable scalar random
sequence. We consider the regression model
yt g(xt,0) = ut, 1 t T, (1) where 0 D
RK is a vector of unknown parameters, the 1 L vectors xt
are...