Hostname: page-component-84b7d79bbc-c654p Total loading time: 0 Render date: 2024-07-29T11:22:21.175Z Has data issue: false hasContentIssue false
  • English
  • Français

LOCAL COMPOSITE QUANTILE REGRESSION SMOOTHING: A FLEXIBLE DATA STRUCTURE AND CROSS-VALIDATION

Published online by Cambridge University Press:  26 March 2020

Xiao Huang  and
Zhongjian Lin
Xiao Huang*
Affiliation:
Kennesaw State University
Zhongjian Lin
Affiliation:
Emory University
*
Address correspondence to Xiao Huang, Department of Economics, Finance and Quantitative Analysis, Kennesaw State University, 560 Parliament Garden Way NW, Kennesaw, GA30144, USA; e-mail: xhuang3@kennesaw.edu.
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper, we study the local composite quantile regression estimator for mixed categorical and continuous data. The local composite quantile estimator is an efficient and safe alternative to the local polynomial method and has been well-studied for continuous covariates. Generalization of the local composite quantile regression estimator to a flexible data structure is appealing to practitioners as empirical studies often encounter categorical data. Furthermore, we study the theoretical properties of the cross-validated bandwidth selection for the local composite quantile estimator. Under mild conditions, we derive the rates of convergence of the cross-validated smoothing parameters to their optimal benchmark values for both categorical and continuous covariates. Monte Carlo experiments show that the proposed estimator may have large efficiency gains compared with the local linear estimator. Furthermore, we illustrate the robustness of the local composite quantile estimator using the Boston housing dataset.

Type
MISCELLANEA
Information
Econometric Theory , Volume 37 , Issue 3 , June 2021 , pp. 613 - 631
Copyright
© Cambridge University Press 2020

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

*

We are grateful to Co-Editor, Liangjun Su, and three anonymous reviewers for their insightful comments and suggestions, which helped improve the paper. We also thank the KSU High Performance Computing Cluster for providing computing support as well as the audience at the 2018 Econometric Society China meeting for their helpful comments. All errors are our own.

References

REFERENCES

Fan, Y., Härdle, W.K., Wang, W. & Zhu, L. (2013) Composite Quantile Regression for the Single-Index Model. Working Paper.CrossRefGoogle Scholar
Guerre, E. & Sabbah, C. (2012) Uniform bias study and Bahadur representation for local polynomial estimators of the conditional quantile function. Econometric Theory 28(1), 87–129.CrossRefGoogle Scholar
Hall, P., Li, Q. & Racine, J.S. (2007) Nonparametric estimation of regression functions in the presence of irrelevant regressors. The Review of Economics and Statistics 89(4), 784–789.CrossRefGoogle Scholar
Hall, P., Racine, J. & Li, Q. (2004) Cross-validation and the estimation of conditional probability densities. Journal of the American Statistical Association 99(468), 1015–1026.CrossRefGoogle Scholar
Jiang, R., Zhou, Z.-G., Qian, W.-M. & Shao, W.-Q. (2012) Single-index composite quantile regression. Journal of the Korean Statistical Society 41(3), 323–332.CrossRefGoogle Scholar
Kai, B., Li, R. & Zou, H. (2010) Local composite quantile regression smoothing: An efficient and safe alternative to local polynomial regression. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 72(1), 49–69.CrossRefGoogle ScholarPubMed
Kai, B., Li, R. & Zou, H. (2011) New efficient estimation and variable selection methods for semiparametric varying-coefficient partially linear models. Annals of Statistics 39(1), 305.CrossRefGoogle ScholarPubMed
Koenker, R. (2005) Quantile Regression. Cambridge University Press.CrossRefGoogle Scholar
Koenker, R. (2017) Quantile regression: 40 years on. Annual Review of Economics 9, 155–176.CrossRefGoogle Scholar
Koenker, R. & Bassett, G. (1978) Regression quantiles. Econometrica 46(1), 33–50.CrossRefGoogle Scholar
Koenker, R., Chernozhukov, V., He, X. & Peng, L. (2017) Handbook of Quantile Regression. CRC Press.CrossRefGoogle Scholar
Kong, E. & Xia, Y. (2014) An adaptive composite quantile approach to dimension reduction. Annals of Statistics 42(4), 1657–1688.CrossRefGoogle Scholar
Li, D. & Li, R. (2016) Local composite quantile regression smoothing for Harris recurrent Markov processes. Journal of Econometrics 194(1), 44–56.CrossRefGoogle ScholarPubMed
Li, Q., Lin, J. & Racine, J.S. (2013) Optimal bandwidth selection for nonparametric conditional distribution and quantile functions. Journal of Business & Economic Statistics 31(1), 57–65.CrossRefGoogle Scholar
Li, Q. & Racine, J. (2004) Cross-validated local linear nonparametric regression. Statistica Sinica 14(2), 485–512.Google Scholar
Li, Q. & Racine, J.S. (2007) Nonparametric Econometrics: Theory and Practice. Princeton University Press.Google Scholar
Pagan, A. & Ullah, A. (1999) Nonparametric Econometrics. Cambridge University Press.CrossRefGoogle Scholar
Racine, J. & Li, Q. (2004) Nonparametric estimation of regression functions with both categorical and continuous data. Journal of Econometrics 119(1), 99–130.CrossRefGoogle Scholar
Ruppert, D. & Wand, M.P. (1994) Multivariate locally weighted least squares regression. Annals of Statistics 22, 1346–1370.CrossRefGoogle Scholar
Su, L., Chen, Y. & Ullah, A. (2009) Functional coefficient estimation with both categorical and continuous data. In Nonparametric Econometric Methods, pp. 131–167. Emerald Group Publishing Limited.CrossRefGoogle Scholar
Zhao, Z. & Xiao, Z. (2014) Efficient regressions via optimally combining quantile information. Econometric Theory 30(6), 1272–1314.CrossRefGoogle ScholarPubMed
Zou, H. & Yuan, M. (2008) Composite quantile regression and the oracle model selection theory. Annals of Statistics 36(3), 1108–1126.CrossRefGoogle Scholar
Supplementary material: File

Huang and Lin Supplementary Materials

Huang and Lin Supplementary Materials 1

Download Huang and Lin Supplementary Materials(File)
File 11.9 KB
Supplementary material: PDF

Huang and Lin Supplementary Materials

Huang and Lin Supplementary Materials 2

Download Huang and Lin Supplementary Materials(PDF)
PDF 376.8 KB