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A nonparametric conditional mode estimate

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  • A. Quintela-Del-Río
  • Ph. Vieu

Abstract

This paper proposes a new nonparametric estimate of the conditional mode. This mode estimate is obtained from kernel smoothing of the first derivative of the conditional density function with location adaptive bandwidth. We give the rates of convergence of this estimate under general dependence conditions on the sample that make our results valid for nonparametric prediction of time series. As a by-products, we also get rate of convergence of the usual mode of a density function under dependence, and we give some extensions to local bandwidth of recent results on kernel estimation under mixing conditions.

Suggested Citation

  • A. Quintela-Del-Río & Ph. Vieu, 1997. "A nonparametric conditional mode estimate," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 8(3), pages 253-266, September.
    • Handle: RePEc:taf:gnstxx:v:8:y:1997:i:3:p:253-266
    DOI: 10.1080/10485259708832723
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    References listed on IDEAS

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    1. Roussas, George G., 1990. "Nonparametric regression estimation under mixing conditions," Stochastic Processes and their Applications, Elsevier, vol. 36(1), pages 107-116, October.
    2. Vieu, Philippe, 1996. "A note on density mode estimation," Statistics & Probability Letters, Elsevier, vol. 26(4), pages 297-307, March.
    3. Young Truong, 1994. "Nonparametric time series regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(2), pages 279-293, June.
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    Cited by:

    1. Kemp, Gordon C.R. & Santos Silva, J.M.C., 2012. "Regression towards the mode," Journal of Econometrics, Elsevier, vol. 170(1), pages 92-101.
    2. Salim Bouzebda & Christophe Chesneau, 2020. "A Note on the Nonparametric Estimation of the Conditional Mode by Wavelet Methods," Stats, MDPI, vol. 3(4), pages 1-9, October.
    3. Hsu, Chih-Yuan & Wu, Tiee-Jian, 2013. "Efficient estimation of the mode of continuous multivariate data," Computational Statistics & Data Analysis, Elsevier, vol. 63(C), pages 148-159.
    4. Said Attaoui, 2014. "Strong uniform consistency rates and asymptotic normality of conditional density estimator in the single functional index modeling for time series data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 98(3), pages 257-286, July.
    5. Ho, Chi-san & Damien, Paul & Walker, Stephen, 2017. "Bayesian mode regression using mixtures of triangular densities," Journal of Econometrics, Elsevier, vol. 197(2), pages 273-283.
    6. Quintela-del-Río, A., 2006. "Nonparametric estimation of the maximum hazard under dependence conditions," Statistics & Probability Letters, Elsevier, vol. 76(11), pages 1117-1124, June.
    7. Gneyou, Kossi Essona, 2014. "A strong linear representation for the maximum conditional hazard rate estimator in survival analysis," Journal of Multivariate Analysis, Elsevier, vol. 128(C), pages 10-18.

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