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A plug-in bandwidth selector for nonparametric quantile regression

Author

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  • Mercedes Conde-Amboage

    (Universidade de Santiago de Compostela)

  • César Sánchez-Sellero

    (Universidade de Santiago de Compostela)

Abstract

In the framework of quantile regression, local linear smoothing techniques have been studied by several authors, particularly by Yu and Jones (J Am Stat Assoc 93:228–237, 1998). The problem of bandwidth selection was addressed in the literature by the usual approaches, such as cross-validation or plug-in methods. Most of the plug-in methods rely on restrictive assumptions on the quantile regression model in relation to the mean regression, or on parametric assumptions. Here we present a plug-in bandwidth selector for nonparametric quantile regression that is defined from a completely nonparametric approach. To this end, the curvature of the quantile regression function and the integrated squared sparsity (inverse of the conditional density) are both nonparametrically estimated. The new bandwidth selector is shown to work well in different simulated scenarios, particularly when the conditions commonly assumed in the literature are not satisfied. A real data application is also given.

Suggested Citation

  • Mercedes Conde-Amboage & César Sánchez-Sellero, 2019. "A plug-in bandwidth selector for nonparametric quantile regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(2), pages 423-450, June.
    • Handle: RePEc:spr:testjl:v:28:y:2019:i:2:d:10.1007_s11749-018-0582-6
    DOI: 10.1007/s11749-018-0582-6
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    References listed on IDEAS

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    1. C. Sánchez-Sellero & W. González-Manteiga & R. Cao, 1999. "Bandwidth Selection in Density Estimation with Truncated and Censored Data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 51(1), pages 51-70, March.
    2. Jones, M. C., 1991. "The roles of ISE and MISE in density estimation," Statistics & Probability Letters, Elsevier, vol. 12(1), pages 51-56, July.
    3. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    4. Abberger, Klaus, 2002. "Variable data driven bandwidth choice in nonparametric quantile regression," CoFE Discussion Papers 02/03, University of Konstanz, Center of Finance and Econometrics (CoFE).
    5. Opsomer, Jean D. & Ruppert, D., 1998. "A Fully Automated Bandwidth Selection Method for Fitting Additive Models," Staff General Research Papers Archive 1176, Iowa State University, Department of Economics.
    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, September.
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