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A Note on the Nonparametric Estimation of the Conditional Mode by Wavelet Methods

Author

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  • Salim Bouzebda

    (Alliance Sorbonne Université, L.M.A.C., Université de Technologie de Compiègne, 60159 Compiègne, France)

  • Christophe Chesneau

    (Department of Mathematics, Université de Caen, LMNO, Campus II, Science 3, 14032 Caen, France)

Abstract

The purpose of this note is to introduce and investigate the nonparametric estimation of the conditional mode using wavelet methods. We propose a new linear wavelet estimator for this problem. The estimator is constructed by combining a specific ratio technique and an established wavelet estimation method. We obtain rates of almost sure convergence over compact subsets of R d . A general estimator beyond the wavelet methodology is also proposed, discussing adaptivity within this statistical framework.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jstats:v:3:y:2020:i:4:p:30-483:d:438501
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    References listed on IDEAS

    as
    1. 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.
    2. M'hamed Ezzahrioui & Elias Ould-Saïd, 2008. "Asymptotic normality of a nonparametric estimator of the conditional mode function for functional data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(1), pages 3-18.
    3. Masry, Elias, 1997. "Multivariate probability density estimation by wavelet methods: Strong consistency and rates for stationary time series," Stochastic Processes and their Applications, Elsevier, vol. 67(2), pages 177-193, May.
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