On monotonicity of regression quantile functions
AbstractIn the linear regression quantile model, the conditional quantile of the response, Y, given x is QYx([tau])[reverse not equivalent]x'[beta]([tau]). Though QYx([tau]) must be monotonically increasing, the Koenker-Bassett regression quantile estimator, , is not monotonic outside a vanishingly small neighborhood of . Given a grid of mesh [delta]n, let be the linear interpolation of the values of along the grid. We show here that for a range of rates, [delta]n, will be strictly monotonic (with probability tending to one) and will be asymptotically equivalent to in the sense that n1/2 times the difference tends to zero at a rate depending on [delta]n.
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 InfoArticle provided by Elsevier in its journal Statistics & Probability Letters.
Volume (Year): 78 (2008)
Issue (Month): 10 (August)
Contact details of provider:
Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description
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.:
- Roger Koenker & Kevin F. Hallock, 2001.
Journal of Economic Perspectives,
American Economic Association, vol. 15(4), pages 143-156, Fall.
- Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
- Portnoy, Stephen, 1991. "Asymptotic behavior of regression quantiles in non-stationary, dependent cases," Journal of Multivariate Analysis, Elsevier, vol. 38(1), pages 100-113, July.
- Peng, Limin, 2012. "Self-consistent estimation of censored quantile regression," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 368-379.
- Zhongjun Qu & Jungmo Yoon, 2011. "Nonparametric Estimation and Inference on Conditional Quantile Processes," Boston University - Department of Economics - Working Papers Series WP2011-059, Boston University - Department of Economics.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Wendy Shamier).
If references are entirely missing, you can add them using this form.