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A crossvalidation method for estimating conditional densities


  • Jianqing Fan
  • Tsz Ho Yim


We extend the idea of crossvalidation to choose the smoothing parameters of the 'double-kernel' local linear regression for estimating a conditional density. Our selection rule optimises the estimated conditional density function by minimising the integrated squared error. We also discuss three other bandwidth selection rules, an ad hoc method used by Fan et al. (1996), a bootstrap method of Hall et al. (1999) for bandwidth selection in the estimation of conditional distribution functions, modified by Bashtannyk & Hyndman (2001) to cover conditional density functions, and finally a simple approach proposed by Hyndman & Yao (2002). The performance of the new approach is compared with these three methods by simulation studies, and our method performs outstandingly well. The method is illustrated by an application to estimating the transition density and the Value-at-Risk of treasury-bill data. Copyright 2004, Oxford University Press.

Suggested Citation

  • Jianqing Fan & Tsz Ho Yim, 2004. "A crossvalidation method for estimating conditional densities," Biometrika, Biometrika Trust, vol. 91(4), pages 819-834, December.
  • Handle: RePEc:oup:biomet:v:91:y:2004:i:4:p:819-834

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    Cited by:

    1. Han-Ying Liang & Jong-Il Baek, 2016. "Asymptotic normality of conditional density estimation with left-truncated and dependent data," Statistical Papers, Springer, vol. 57(1), pages 1-20, March.
    2. Kasahara, Hiroyuki & Liang, Yawen & Rodrigue, Joel, 2016. "Does importing intermediates increase the demand for skilled workers? Plant-level evidence from Indonesia," Journal of International Economics, Elsevier, vol. 102(C), pages 242-261.
    3. Han-Ying Liang & Jong-Il Baek, 2016. "Asymptotic normality of conditional density estimation with left-truncated and dependent data," Statistical Papers, Springer, vol. 57(1), pages 1-20, March.
    4. Gery Geenens & Richard Dunn, 2017. "A nonparametric copula approach to conditional Value-at-Risk," Papers 1712.05527,, revised Oct 2019.
    5. Ann-Kathrin Bott & Michael Kohler, 2017. "Nonparametric estimation of a conditional density," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(1), pages 189-214, February.
    6. Liang, Han-Ying & Peng, Liang, 2010. "Asymptotic normality and Berry-Esseen results for conditional density estimator with censored and dependent data," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1043-1054, May.
    7. Ming-Yueh Huang & Chin-Tsang Chiang, 2017. "An Effective Semiparametric Estimation Approach for the Sufficient Dimension Reduction Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1296-1310, July.
    8. Arora, Siddharth & Taylor, James W., 2016. "Forecasting electricity smart meter data using conditional kernel density estimation," Omega, Elsevier, vol. 59(PA), pages 47-59.
    9. Janssen, Paul & Swanepoel, Jan & Veraverbeke, Noël, 2017. "Smooth copula-based estimation of the conditional density function with a single covariate," Journal of Multivariate Analysis, Elsevier, vol. 159(C), pages 39-48.
    10. Chopin, Nicolas & Gadat, Sébastien & Guedj, Benjamin & Guyader, Arnaud & Vernet, Elodie, 2015. "On some recent advances in high dimensional Bayesian Statistics," TSE Working Papers 15-557, Toulouse School of Economics (TSE).
    11. Ann-Kathrin Bott & Michael Kohler, 2016. "Adaptive Estimation of a Conditional Density," International Statistical Review, International Statistical Institute, vol. 84(2), pages 291-316, August.
    12. Frank A. Cowell & Emmanuel Flachaire, 2014. "Statistical Methods for Distributional Analysis," Working Papers halshs-01115996, HAL.
    13. Song, Zhaogang & Xiu, Dacheng, 2016. "A tale of two option markets: Pricing kernels and volatility risk," Journal of Econometrics, Elsevier, vol. 190(1), pages 176-196.
    14. Holmes, Michael P. & Gray, Alexander G. & Isbell Jr., Charles Lee, 2010. "Fast kernel conditional density estimation: A dual-tree Monte Carlo approach," Computational Statistics & Data Analysis, Elsevier, vol. 54(7), pages 1707-1718, July.
    15. Tang, Yongqiang & Ghosal, Subhashis, 2007. "A consistent nonparametric Bayesian procedure for estimating autoregressive conditional densities," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4424-4437, May.
    16. Kateřina Konečná & Ivanka Horová, 2019. "Maximum likelihood method for bandwidth selection in kernel conditional density estimate," Computational Statistics, Springer, vol. 34(4), pages 1871-1887, December.
    17. Wen, Kuangyu & Wu, Ximing, 2017. "Smoothed kernel conditional density estimation," Economics Letters, Elsevier, vol. 152(C), pages 112-116.
    18. Liang, Han-Ying & Liu, Ai-Ai, 2013. "Kernel estimation of conditional density with truncated, censored and dependent data," Journal of Multivariate Analysis, Elsevier, vol. 120(C), pages 40-58.
    19. Otneim, Håkon & Tjøstheim, Dag, 2016. "Non-parametric estimation of conditional densities: A new method," Discussion Papers 2016/22, Norwegian School of Economics, Department of Business and Management Science.
    20. Ichimura, Tsuyoshi & Fukuda, Daisuke, 2010. "A fast algorithm for computing least-squares cross-validations for nonparametric conditional kernel density functions," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3404-3410, December.
    21. Taylor, James W. & Jeon, Jooyoung, 2015. "Forecasting wind power quantiles using conditional kernel estimation," Renewable Energy, Elsevier, vol. 80(C), pages 370-379.
    22. Wang, Xiao-Feng & Ye, Deping, 2015. "Conditional density estimation in measurement error problems," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 38-50.
    23. Giwhyun Lee & Yu Ding & Marc G. Genton & Le Xie, 2015. "Power Curve Estimation With Multivariate Environmental Factors for Inland and Offshore Wind Farms," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 56-67, March.
    24. Faugeras, Olivier P., 2009. "A quantile-copula approach to conditional density estimation," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 2083-2099, October.
    25. Jooyoung Jeon & James W. Taylor, 2012. "Using Conditional Kernel Density Estimation for Wind Power Density Forecasting," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(497), pages 66-79, March.

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