Flexible modeling based on copulas in nonparametric median regression
Consider the model Y=m(X)+[epsilon], where m([dot operator])=med(Y[dot operator]) is unknown but smooth. It is often assumed that [epsilon] and X are independent. However, in practice this assumption is violated in many cases. In this paper we propose modeling the dependence between [epsilon] and X by means of a copula model, i.e., where is a copula function depending on an unknown parameter [theta], and F[epsilon] and FX are the marginals of [epsilon] and X. Since many parametric copula families contain the independent copula as a special case, the so-obtained regression model is more flexible than the 'classical' regression model. We estimate the parameter [theta] via a pseudo-likelihood method and prove the asymptotic normality of the estimator, based on delicate empirical process theory. We also study the estimation of the conditional distribution of Y given X. The procedure is illustrated by means of a simulation study, and the method is applied to data on food expenditures in households.
Volume (Year): 100 (2009)
Issue (Month): 6 (July)
|Contact details of provider:|| Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description|
|Order Information:|| Postal: http://www.elsevier.com/wps/find/supportfaq.cws_home/regional|
References listed on IDEAS
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.:
- repec:ner:tilbur:urn:nbn:nl:ui:12-192435 is not listed on IDEAS
- Xiaohong Chen & Oliver Linton & Ingrid Van Keilegom, 2003.
"Estimation of Semiparametric Models when the Criterion Function Is Not Smooth,"
Econometric Society, vol. 71(5), pages 1591-1608, 09.
- Xiaohong Chen & Oliver Linton & Ingrid Van Keilegom, 2003. "Estimation of Semiparametric Models when the Criterion Function is not Smooth," STICERD - Econometrics Paper Series /2003/450, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
- Xiaohong Chen & Oliver Linton & Ingrid Van Keilegom, 2003. "Estimation of semiparametric models when the criterion function is not smooth," LSE Research Online Documents on Economics 2167, London School of Economics and Political Science, LSE Library.
- Xiaohong Chen & Oliver Linton & Ingred Van Keilegom, 2002. "Estimation of semiparametric models when the criterion function is not smooth," CeMMAP working papers CWP02/02, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
- repec:ner:tilbur:urn:nbn:nl:ui:12-192434 is not listed on IDEAS
- Olivier Scaillet, 2005.
"Kernel Based Goodness-of-Fit Tests for Copulas with Fixed Smoothing Parameters,"
FAME Research Paper Series
rp145, International Center for Financial Asset Management and Engineering.
- Scaillet, Olivier, 2007. "Kernel-based goodness-of-fit tests for copulas with fixed smoothing parameters," Journal of Multivariate Analysis, Elsevier, vol. 98(3), pages 533-543, March.
- Xiaohong Chen & Yanqin Fan & Victor Tsyrennifov, 2004.
"Efficient Estimation of Semiparametric Multivariate Copula Models,"
Vanderbilt University Department of Economics Working Papers
0420, Vanderbilt University Department of Economics.
- Chen, Xiaohong & Fan, Yanqin & Tsyrennikov, Viktor, 2006. "Efficient Estimation of Semiparametric Multivariate Copula Models," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1228-1240, September.
- Charpentier, Arthur & Segers, Johan, 2007. "Lower tail dependence for Archimedean copulas: Characterizations and pitfalls," Insurance: Mathematics and Economics, Elsevier, vol. 40(3), pages 525-532, May.
- Einmahl, J.H.J. & van Keilegom, I., 2006.
"Tests for Independence in Nonparametric Regression,"
2006-80, Tilburg University, Center for Economic Research.
- Einmahl, J.H.J. & van Keilegom, I., 2008. "Tests for independence in nonparametric regression," Other publications TiSEM 4356c520-d1d5-4156-b5b7-0, Tilburg University, School of Economics and Management.
- Einmahl, John H.J. & Van Keilegom, Ingrid, 2008.
"Specification tests in nonparametric regression,"
Journal of Econometrics,
Elsevier, vol. 143(1), pages 88-102, March.
- Ling Hu, 2006. "Dependence patterns across financial markets: a mixed copula approach," Applied Financial Economics, Taylor & Francis Journals, vol. 16(10), pages 717-729.
- Chen, Xiaohong & Fan, Yanqin, 2007. "A Model Selection Test For Bivariate Failure-Time Data," Econometric Theory, Cambridge University Press, vol. 23(03), pages 414-439, June.
- repec:ner:tilbur:urn:nbn:nl:ui:12-383455 is not listed on IDEAS
- Fermanian, Jean-David, 2005. "Goodness-of-fit tests for copulas," Journal of Multivariate Analysis, Elsevier, vol. 95(1), pages 119-152, July.
When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:100:y:2009:i:6:p:1270-1281. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)
If references are entirely missing, you can add them using this form.