Nonparametric Estimation and Inference on Conditional Quantile Processes
AbstractWe consider the estimation and inference about a nonparametrically specified con- ditional quantile process. For estimation, a two-step procedure is proposed. The first step utilizes local linear regressions and maintains quantile monotonicity through sim- ple inequality constraints. The second step involves linear interpolation between adja- cent quantiles. When computing the estimator, the bandwidth parameter is allowed to vary across quantiles to adapt to the data sparsity. The procedure is computationally simple to implement and is feasible even for relatively large data sets. For inference, we first obtain a uniform Bahadur-type representation for the conditional quantile process. Then, we show that the estimator converges weakly to a continuous Gaussian process, whose critical values can be estimated via simulations by exploiting the fact that it is conditionally pivotal. Next, we demonstrate how to compute the optimal bandwidth, construct uniform confidence bands and test hypotheses about the quantile process. Finally, we examine the performance of the bandwidth selection rule and the uniform confidence bands through simulations.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Boston University - Department of Economics in its series Boston University - Department of Economics - Working Papers Series with number WP2011-059.
Length: 62 pages
Date of creation: Jan 2011
Date of revision:
nonparametric quantile regression; monotonicity constraint; uniform Bahadur representation; uniform inference;
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Härdle, Wolfgang K. & Song, Song, 2010. "Confidence Bands In Quantile Regression," Econometric Theory, Cambridge University Press, vol. 26(04), pages 1180-1200, August.
- Chernozhukov, Victor & Hansen, Christian & Jansson, Michael, 2009. "Finite sample inference for quantile regression models," Journal of Econometrics, Elsevier, vol. 152(2), pages 93-103, October.
- Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
- Howard D. Bondell & Brian J. Reich & Huixia Wang, 2010. "Noncrossing quantile regression curve estimation," Biometrika, Biometrika Trust, vol. 97(4), pages 825-838.
- Koenker,Roger, 2005.
Cambridge University Press, number 9780521608275, December.
- Victor Chernozhukov & Iv·n Fern·ndez-Val & Alfred Galichon, 2010.
"Quantile and Probability Curves Without Crossing,"
Econometric Society, vol. 78(3), pages 1093-1125, 05.
- Victor Chernozhukov & Ivan Fernandez-Val & Alfred Galichon, 2007. "Quantile And Probability Curves Without Crossing," Boston University - Department of Economics - Working Papers Series WP2007-011, Boston University - Department of Economics.
- Victor Chernozhukov & Ivan Fernandez-Val & Alfred Galichon, 2007. "Quantile and probability curves without crossing," CeMMAP working papers CWP10/07, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
- Victor Chernozhukov & Ivan Fernandez-Val & Alfred Galichon, 2010. "Quantile and Probability Curves without Crossing," Sciences Po publications info:hdl:2441/5rkqqmvrn4t, Sciences Po.
- Garry F. Barrett & Stephen G. Donald, 2003. "Consistent Tests for Stochastic Dominance," Econometrica, Econometric Society, vol. 71(1), pages 71-104, January.
- Neocleous, Tereza & Portnoy, Stephen, 2008. "On monotonicity of regression quantile functions," Statistics & Probability Letters, Elsevier, vol. 78(10), pages 1226-1229, August.
- Sergio Firpo, 2007.
"Efficient Semiparametric Estimation of Quantile Treatment Effects,"
Econometric Society, vol. 75(1), pages 259-276, 01.
- Sergio Firpo, 2004. "Efficient Semiparametric Estimation of Quantile Treatment Effects," Econometric Society 2004 North American Summer Meetings 605, Econometric Society.
- Bai, Jushan, 1996. "Testing for Parameter Constancy in Linear Regressions: An Empirical Distribution Function Approach," Econometrica, Econometric Society, vol. 64(3), pages 597-622, May.
- Roger Koenker & Zhijie Xiao, 2002. "Inference on the Quantile Regression Process," Econometrica, Econometric Society, vol. 70(4), pages 1583-1612, July.
- Zhongjun Qu & Tatsushi Oka, 2010.
"Estimating structural changes in regression quantiles,"
Boston University - Department of Economics - Working Papers Series
WP2010-052, Boston University - Department of Economics.
- Oka, Tatsushi & Qu, Zhongjun, 2011. "Estimating structural changes in regression quantiles," Journal of Econometrics, Elsevier, vol. 162(2), pages 248-267, June.
- Holger Dette & Stanislav Volgushev, 2008. "Non-crossing non-parametric estimates of quantile curves," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(3), pages 609-627.
- Heckman, James J & Smith, Jeffrey, 1997. "Making the Most Out of Programme Evaluations and Social Experiments: Accounting for Heterogeneity in Programme Impacts," Review of Economic Studies, Wiley Blackwell, vol. 64(4), pages 487-535, October.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Courtney Sullivan).
If references are entirely missing, you can add them using this form.