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Single-index quantile regression

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  • Wu, Tracy Z.
  • Yu, Keming
  • Yu, Yan
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    Abstract

    Nonparametric quantile regression with multivariate covariates is a difficult estimation problem due to the "curse of dimensionality". To reduce the dimensionality while still retaining the flexibility of a nonparametric model, we propose modeling the conditional quantile by a single-index function , where a univariate link function g0([dot operator]) is applied to a linear combination of covariates , often called the single-index. We introduce a practical algorithm where the unknown link function g0([dot operator]) is estimated by local linear quantile regression and the parametric index is estimated through linear quantile regression. Large sample properties of estimators are studied, which facilitate further inference. Both the modeling and estimation approaches are demonstrated by simulation studies and real data applications.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 101 (2010)
    Issue (Month): 7 (August)
    Pages: 1607-1621

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    Handle: RePEc:eee:jmvana:v:101:y:2010:i:7:p:1607-1621

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    Related research

    Keywords: Conditional quantile Dimension reduction Local polynomial smoothing Nonparametric model Semiparametric model;

    References

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    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.:
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    1. Joel Horowitz & Sokbae 'Simon' Lee, 2004. "Nonparametric estimation of an additive quantile regression model," CeMMAP working papers CWP07/04, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    2. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    3. De Gooijer J.G. & Zerom D., 2003. "On Additive Conditional Quantiles With High Dimensional Covariates," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 135-146, January.
    4. Xia, Yingcun & Härdle, Wolfgang, 2006. "Semi-parametric estimation of partially linear single-index models," Journal of Multivariate Analysis, Elsevier, vol. 97(5), pages 1162-1184, May.
    5. Roger Koenker & Kevin F. Hallock, 2001. "Quantile Regression," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 143-156, Fall.
    6. 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.
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    Citations

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    Cited by:
    1. Hidehiko Ichimura & Sokbae Lee, 2006. "Characterization of the Asymptotic Distribution of Semiparametric M-Estimators," CIRJE F-Series CIRJE-F-426, CIRJE, Faculty of Economics, University of Tokyo.
    2. Efang Kong & Oliver Linton & Yingcun Xia, 2011. "Global Bahadur representation for nonparametric censored regression quantiles and its applications," CeMMAP working papers CWP33/11, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

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