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

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  • Salim Bouzebda
  • Sultana Didi

Abstract

In the present paper, we are mainly concerned with the non parametric estimation of the density as well as the regression function by using orthonormal wavelet bases. We provide the strong uniform consistency properties with rates of these estimators, over compact subsets of Rd$\mathbb {R}^{d}$, 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.

Suggested Citation

  • Salim Bouzebda & Sultana Didi, 2017. "Multivariate wavelet density and regression estimators for stationary and ergodic discrete time processes: Asymptotic results," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(3), pages 1367-1406, February.
    • Handle: RePEc:taf:lstaxx:v:46:y:2017:i:3:p:1367-1406
    DOI: 10.1080/03610926.2015.1019144
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    Cited by:

    1. Sultana Didi & Salim Bouzebda, 2022. "Wavelet Density and Regression Estimators for Continuous Time Functional Stationary and Ergodic Processes," Mathematics, MDPI, vol. 10(22), pages 1-37, November.
    2. Nour-Eddine Berrahou & Salim Bouzebda & Lahcen Douge, 2024. "The Bahadur Representation for Empirical and Smooth Quantile Estimators Under Association," Methodology and Computing in Applied Probability, Springer, vol. 26(2), pages 1-37, June.
    3. Salim Bouzebda & Mohamed Chaouch & Sultana Didi Biha, 2022. "Asymptotics for function derivatives estimators based on stationary and ergodic discrete time processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(4), pages 737-771, August.
    4. Krebs, Johannes T.N., 2018. "Nonparametric density estimation for spatial data with wavelets," Journal of Multivariate Analysis, Elsevier, vol. 166(C), pages 300-319.

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