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)
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- 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.
- 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 & 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.
- 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 & Ingrid Van Keilegom, 2003. "Estimation of Semiparametric Models when the Criterion Function is not Smooth," STICERD - Econometrics Paper Series 450, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
- 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., 2008.
"Specification tests in nonparametric regression,"
Other publications TiSEM
2c94c2d8-8305-4fb1-b47f-7, Tilburg University, School of Economics and Management.
- 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.
- 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.
- 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.
- Fermanian, Jean-David, 2005. "Goodness-of-fit tests for copulas," Journal of Multivariate Analysis, Elsevier, vol. 95(1), pages 119-152, July.
- Ling Hu, 2006. "Dependence patterns across financial markets: a mixed copula approach," Applied Financial Economics, Taylor & Francis Journals, vol. 16(10), pages 717-729.
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