Local Constant and Local Bilinear Multiple-Output Quantile Regression
AbstractA new quantile regression concept, based on a directional version of Koenker and Bassett’s traditional single-output one, has been introduced in [Hallin, Paindaveine and ¡Siman, Annals of Statistics 2010, 635-703] for multiple-output regression problems. The polyhedral contours provided by the empirical counterpart of that concept, however, cannot adapt to nonlinear and/or heteroskedastic dependencies. This paper therefore introduces local constant and local linear versions of those contours, which both allow to asymptotically recover the conditional halfspace depth contours of the response. In the multiple-output context considered, the local linear construction actually is of a bilinear nature. Bahadur representation and asymptotic normality results are established. Illustrations are provided both on simulated and real data.
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Bibliographic InfoPaper provided by ULB -- Universite Libre de Bruxelles in its series Working Papers ECARES with number ECARES 2012-003.
Length: 41 p.
Date of creation: Jan 2012
Date of revision:
Publication status: Published by:
nonparametric regression; local bilineear regression; quantile regression; multivariate quantile; growth chart; halfspace depth;
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- Ioannides, D. A., 2004. "Fixed design regression quantiles for time series," Statistics & Probability Letters, Elsevier, vol. 68(3), pages 235-245, July.
- Keming Yu & Zudi Lu, 2004. "Local Linear Additive Quantile Regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association, vol. 31(3), pages 333-346.
- Marc Hallin & Davy Paindaveine & Miroslav Šiman, 2010.
"Multivariate quantiles and multiple-output regression quantiles: From L1 optimization to halfspace depth,"
ULB Institutional Repository
2013/127979, ULB -- Universite Libre de Bruxelles.
- Marc Hallin & Davy Paindaveine & Miroslav Siman, 2008. "Multivariate quantiles and multiple-output regression quantiles: from L1 optimization to halfspace depth," Working Papers ECARES 2008_042, ULB -- Universite Libre de Bruxelles.
- Struyf, Anja J. & Rousseeuw, Peter J., 1999. "Halfspace Depth and Regression Depth Characterize the Empirical Distribution," Journal of Multivariate Analysis, Elsevier, vol. 69(1), pages 135-153, April.
- Yu, Keming & Jones, M. C., 1997. "A comparison of local constant and local linear regression quantile estimators," Computational Statistics & Data Analysis, Elsevier, vol. 25(2), pages 159-166, July.
- Davy Paindaveine & Miroslav Siman, 2009.
"On directional multiple-output quantile regression,"
Working Papers ECARES
2009_011, ULB -- Universite Libre de Bruxelles.
- Paindaveine, Davy & Siman, Miroslav, 2011. "On directional multiple-output quantile regression," Journal of Multivariate Analysis, Elsevier, vol. 102(2), pages 193-212, February.
- Toshio Honda, 2000. "Nonparametric Estimation of a Conditional Quantile for α-Mixing Processes," Annals of the Institute of Statistical Mathematics, Springer, vol. 52(3), pages 459-470, September.
- Härdle, Wolfgang K. & Song, Song, 2010. "Confidence Bands In Quantile Regression," Econometric Theory, Cambridge University Press, vol. 26(04), pages 1180-1200, August.
- Koenker, Roger & Zhao, Quanshui, 1996. "Conditional Quantile Estimation and Inference for Arch Models," Econometric Theory, Cambridge University Press, vol. 12(05), pages 793-813, December.
- Kong, Efang & Linton, Oliver & Xia, Yingcun, 2010.
"Uniform Bahadur Representation For Local Polynomial Estimates Of M-Regression And Its Application To The Additive Model,"
Cambridge University Press, vol. 26(05), pages 1529-1564, October.
- Efang Kong & Oliver Linton & Yingcun Xia, 2009. "Uniform Bahadur Representation for LocalPolynomial Estimates of M-Regressionand Its Application to The Additive Model," STICERD - Econometrics Paper Series /2009/535, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
- Wei, Ying, 2008. "An Approach to Multivariate Covariate-Dependent Quantile Contours With Application to Bivariate Conditional Growth Charts," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 397-409, March.
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