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Optimal Bandwidth Selection for Nonparametric Conditional Distribution and Quantile Functions

  • Qi Li
  • Juan Lin
  • Jeffrey S. Racine

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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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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  1. Victor Chernozhukov & Ivan Fernandez-Val & Alfred Galichon, 2007. "Quantile And Probability Curves Without Crossing," Boston University - Department of Economics - Working Papers Series WP2007-011, Boston University - Department of Economics.
  2. Cai, Zongwu, 2002. "Regression Quantiles For Time Series," Econometric Theory, Cambridge University Press, vol. 18(01), pages 169-192, February.
  3. 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.
  4. 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.
  5. 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.
  6. Hayfield, Tristen & Racine, Jeffrey S., 2008. "Nonparametric Econometrics: The np Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 27(i05).
  7. 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.
  8. repec:jss:jstsof:27:i05 is not listed on IDEAS
  9. Roger Koenker & Kevin F. Hallock, 2001. "Quantile Regression," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 143-156, Fall.
  10. Esfandiar Maasoumi & Maria Ana Lugo, 2008. "The Information Basis of Multivariate Poverty Assessments," Emory Economics 0804, Department of Economics, Emory University (Atlanta).
  11. 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.
  12. 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.
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