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On Conditional Density Estimation

Author

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  • Jan G. de Gooijer
  • Dawit Zerom

    (Faculty of Economics and Econometrics, University of Amsterdam)

Abstract

With the aim to mitigate the possibleproblem of negativity in the estimation of the conditionaldensity function, we introduce a so-called re-weightedNadaraya-Watson (RNW) estimator. The proposed RNWestimator is constructed by a slight modificationof the well-known Nadaraya-Watson smoother.Because the estimator is explicitly defined in terms ofthe data, its practical implementation is quite simple.With a detailed asymptotic analysis, we demonstratethat the RNW smoother preserves thesuperior large-sample bias property of thelocal linear smoother of the conditional densityproposed by Fan, Yao and Tong (1996).As a matter of independent statistical interest,the limit distribution of the RNW estimator is alsoderived.

Suggested Citation

  • Jan G. de Gooijer & Dawit Zerom, 2002. "On Conditional Density Estimation," Tinbergen Institute Discussion Papers 02-032/4, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20020032
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    References listed on IDEAS

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    1. Chen, Xiaohong & Linton, Oliver & Robinson, Peter, 2001. "The estimation of conditional densities," LSE Research Online Documents on Economics 2312, London School of Economics and Political Science, LSE Library.
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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. Jonas Rothfuss & Fabio Ferreira & Simon Walther & Maxim Ulrich, 2019. "Conditional Density Estimation with Neural Networks: Best Practices and Benchmarks," Papers 1903.00954, arXiv.org, revised Apr 2019.
    3. 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.
    4. 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.
    5. A. Delaigle & P. Hall, 2016. "Approximating fragmented functional data by segments of Markov chains," Biometrika, Biometrika Trust, vol. 103(4), pages 779-799.
    6. Akkal Fatima & Kadiri Nadia & Rabhi Abbes, 2021. "Asymptotic Normality of Conditional Density and Conditional Mode in the Functional Single Index Model," Econometrics. Advances in Applied Data Analysis, Sciendo, vol. 25(1), pages 1-24, March.
    7. 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.
    8. 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.
    9. Wen, Kuangyu & Wu, Ximing, 2017. "Smoothed kernel conditional density estimation," Economics Letters, Elsevier, vol. 152(C), pages 112-116.
    10. João Henrique Gonçalves Mazzeu & Esther Ruiz & Helena Veiga, 2018. "Uncertainty And Density Forecasts Of Arma Models: Comparison Of Asymptotic, Bayesian, And Bootstrap Procedures," Journal of Economic Surveys, Wiley Blackwell, vol. 32(2), pages 388-419, April.
    11. 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.
    12. Xiong, Xianzhu & Ou, Meijuan & Chen, Ailian, 2021. "Reweighted Nadaraya–Watson estimation of conditional density function in the right-censored model," Statistics & Probability Letters, Elsevier, vol. 168(C).
    13. repec:ebl:ecbull:v:3:y:2007:i:62:p:1-6 is not listed on IDEAS
    14. Wang, Xiao-Feng & Ye, Deping, 2015. "Conditional density estimation in measurement error problems," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 38-50.
    15. Manzan, Sebastiano & Zerom, Dawit, 2008. "A bootstrap-based non-parametric forecast density," International Journal of Forecasting, Elsevier, vol. 24(3), pages 535-550.
    16. De Gooijer, Jan G. & Henter, Gustav Eje & Yuan, Ao, 2022. "Kernel-based hidden Markov conditional densities," Computational Statistics & Data Analysis, Elsevier, vol. 169(C).
    17. Michael Kohler & Adam Krzyżak, 2020. "Estimating quantiles in imperfect simulation models using conditional density estimation," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(1), pages 123-155, February.
    18. Gonçalves Mazzeu, Joao Henrique & Ruiz Ortega, Esther & Veiga, Helena, 2015. "Model uncertainty and the forecast accuracy of ARMA models: A survey," DES - Working Papers. Statistics and Econometrics. WS ws1508, Universidad Carlos III de Madrid. Departamento de Estadística.
    19. Kim Huynh & David Jacho-Chavez, 2007. "Conditional density estimation: an application to the Ecuadorian manufacturing sector," Economics Bulletin, AccessEcon, vol. 3(62), pages 1-6.

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    More about this item

    Keywords

    alpha-mixing; asymptotic properties; negativity; nonparametric; re-weighted;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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