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Multivariate wavelet density and regression estimators for stationary and ergodic continuous time processes: Asymptotic results

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Abstract

In the present paper, we are mainly concerned with the nonparametric estimation of the density as well as the regression function, related to stationary and ergodic continuous time processes, by using orthonormal wavelet bases. We provide the strong uniform consistency properties with rates of these estimators, over compact subsets of ℝd, under a general ergodic condition on the underlying processes. We characterize the asymptotic normality of considered wavelet-based estimators under easily verifiable conditions. The asymptotic properties of these estimators are obtained by means of the martingale approach.

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Authors and Affiliations

  1. Sorbonne Univ., Univ. de Technol. de Compiègne, Compiègne, France

    S. Bouzebda

  2. Univ. Pierre et Marie Curie, Paris, France

    S. Didi & L. El Hajj

Authors
  1. S. Bouzebda
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  2. S. Didi
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  3. L. El Hajj
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Correspondence to S. Bouzebda.

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Bouzebda, S., Didi, S. & El Hajj, L. Multivariate wavelet density and regression estimators for stationary and ergodic continuous time processes: Asymptotic results. Math. Meth. Stat. 24, 163–199 (2015). https://doi.org/10.3103/S1066530715030011

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  • DOI: https://doi.org/10.3103/S1066530715030011

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