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Optimal Bandwidth Selection for Nonparametric Conditional Distribution and Quantile Functions

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  • Qi Li
  • Juan Lin
  • Jeffrey S. Racine

Abstract

We propose a data-driven least squares cross-validation method to optimally select smoothing parameters for the nonparametric estimation of conditional cumulative distribution functions and conditional quantile functions. We allow for general multivariate covariates that can be continuous, categorical or a mix of either. We provide asymptotic analysis, examine finite-sample properties via Monte Carlo simulation, and consider an application involving testing for first order stochastic dominance of children's health conditional on parental education and income.

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File URL: http://socserv.mcmaster.ca/econ/rsrch/papers/archive/2012-10.pdf
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Bibliographic Info

Paper provided by McMaster University in its series Department of Economics Working Papers with number 2012-10.

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Length: 37 pages
Date of creation: Oct 2012
Date of revision:
Handle: RePEc:mcm:deptwp:2012-10

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References

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  1. Victor Chernozhukov & Ivan Fernandez-Val & Alfred Galichon, 2007. "Quantile and probability curves without crossing," CeMMAP working papers CWP10/07, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  2. Roger Koenker & Kevin F. Hallock, 2001. "Quantile Regression," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 143-156, Fall.
  3. Peter Hall & Qi Li & Jeffrey S. Racine, 2007. "Nonparametric Estimation of Regression Functions in the Presence of Irrelevant Regressors," The Review of Economics and Statistics, MIT Press, vol. 89(4), pages 784-789, November.
  4. Peter Hall & Jeff Racine & Qi Li, 2004. "Cross-Validation and the Estimation of Conditional Probability Densities," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 1015-1026, December.
  5. Hyndman, R.J. & Yao, Q., 1998. "Nonparametric Estimation and Symmetry Tests for Conditional Density Functions," Monash Econometrics and Business Statistics Working Papers 17/98, Monash University, Department of Econometrics and Business Statistics.
  6. Bashtannyk, D.M. & Hyndman, R.J., 1998. "Bandwidth Selection for Kernel Conditional Density Estimation," Monash Econometrics and Business Statistics Working Papers 16/98, Monash University, Department of Econometrics and Business Statistics.
  7. Tristen Hayfield & Jeffrey S. Racine, . "Nonparametric Econometrics: The np Package," Journal of Statistical Software, American Statistical Association, vol. 27(i05).
  8. Racine, Jeff & Li, Qi, 2004. "Nonparametric estimation of regression functions with both categorical and continuous data," Journal of Econometrics, Elsevier, vol. 119(1), pages 99-130, March.
  9. Li, Qi & Racine, Jeffrey S, 2008. "Nonparametric Estimation of Conditional CDF and Quantile Functions With Mixed Categorical and Continuous Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 423-434.
  10. Maasoumi, Esfandiar & Lugo, Maria, 2006. "The Information Basis of Multivariate Poverty Assessments," Departmental Working Papers 0603, Southern Methodist University, Department of Economics.
  11. Cai, Zongwu, 2002. "Regression Quantiles For Time Series," Econometric Theory, Cambridge University Press, vol. 18(01), pages 169-192, February.
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Citations

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Cited by:
  1. Jeffrey S. Racine, 2013. "Mixed Data Kernel Copulas," Department of Economics Working Papers 2013-12, McMaster University.
  2. Long, Wei & Ouyang, Min & Shang, Ying, 2013. "Efficient estimation of partially linear varying coefficient models," Economics Letters, Elsevier, vol. 121(1), pages 79-81.
  3. Shih-Kang Chao & Katharina Proksch & Holger Dette & Wolfgang Härdle, 2014. "Confidence Corridors for Multivariate Generalized Quantile Regression," SFB 649 Discussion Papers SFB649DP2014-028, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.

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