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The Estimation of Conditional Densities

Author

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  • Xiaohong Chen
  • Oliver Linton
  • Peter M Robinson

Abstract

We discuss a number of issues in the smoothed nonparametric estimation of kernel conditional probability density functions for stationary processes. The kernel conditional density estimate is a ratio of joint and marginal density estimates. We point out the different implications of leading choices of bandwidths in numerator and denominator for the ability of the estimate to integrate to one and to have finite moments. Again bearing in mind different bandwidth possibilities, we discuss asymptotic theory for the estimate: asymptotic bias and variance are calculated under various conditions, an extended discussion of bandwidth choice is included, and a central limit theorem is given.

Suggested Citation

  • Xiaohong Chen & Oliver Linton & Peter M Robinson, 2001. "The Estimation of Conditional Densities," STICERD - Econometrics Paper Series 415, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    • Handle: RePEc:cep:stiecm:415
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    File URL: https://sticerd.lse.ac.uk/dps/em/em415.pdf
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    Cited by:

    1. Jan G. De Gooijer & Dawit Zerom, 2003. "On Conditional Density Estimation," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 57(2), pages 159-176, May.
    2. 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.
    3. Mercedes Esteban-Bravo & Jose M. Vidal-Sanz & Gökhan Yildirim, 2014. "Valuing Customer Portfolios with Endogenous Mass and Direct Marketing Interventions Using a Stochastic Dynamic Programming Decomposition," Marketing Science, INFORMS, vol. 33(5), pages 621-640, September.
    4. Tindara Addabbo & Donata Favaro & Stefano Magrini, 2012. "Gender differences in productivity rewards: the role of human capital," International Review of Economics, Springer;Happiness Economics and Interpersonal Relations (HEIRS), vol. 59(1), pages 81-110, March.
    5. Alejandro Quintela-Del-Río, 2008. "Hazard function given a functional variable: Non-parametric estimation under strong mixing conditions," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(5), pages 413-430.
    6. Favaro, Donata & Magrini, Stefano, 2008. "Group versus individual discrimination among young workers: A distributional approach," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 37(5), pages 1856-1879, October.
    7. Yulia Kotlyarova & Marcia M. A. Schafgans & Victoria Zinde-Walsh, 2021. "Rates of Expansions for Functional Estimators," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 19(1), pages 121-139, December.
    8. Buch-Kromann, Tine & Guillén, Montserrat & Linton, Oliver & Nielsen, Jens Perch, 2011. "Multivariate density estimation using dimension reducing information and tail flattening transformations," Insurance: Mathematics and Economics, Elsevier, vol. 48(1), pages 99-110, January.
    9. Amaro de Matos, Joao & Fernandes, Marcelo, 2007. "Testing the Markov property with high frequency data," Journal of Econometrics, Elsevier, vol. 141(1), pages 44-64, November.
    10. Corradi, Valentina & Distaso, Walter & Fernandes, Marcelo, 2012. "International market links and volatility transmission," Journal of Econometrics, Elsevier, vol. 170(1), pages 117-141.
    11. 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.
    12. Tindara Addabbo & Donata Favaro & Stefano Magrini, 2010. "Gender differences in productivity rewards in Italy: the role of human capital," Working Papers 2010_11, Department of Economics, University of Venice "Ca' Foscari".

    More about this item

    Keywords

    Conditional density estimation; serial dependence; bandwidth choice.;
    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

    Statistics

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