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Asymptotic results for the regression function estimate on continuous time stationary and ergodic data

Author

Listed:
  • Didi Sultana

    (LSTA, Université de Paris 6, 4, Place Jussieu, 75252 Paris, France)

  • Louani Djamal

    (LSTA, Université de Paris 6, 4, Place Jussieu, 75252 Paris, France)

Abstract

This paper is devoted to the study of asymptotic properties of the regression function kernel estimate in the setting of continuous time stationary and ergodic data. More precisely, considering the Nadaraya–Watson type estimator, say m̂T(x), of the l-indexed regression function m(x) =𝔼 (l(Y)|X = x) built upon continuous time stationary and ergodic data (Xt, Yt)0≤t≤T, we establish its pointwise and uniform, over a dilative compact set, convergences with rates. Notice that the ergodic setting covers and completes various situations as compared to the mixing case and stands as more convenient to use in practice.

Suggested Citation

  • Didi Sultana & Louani Djamal, 2014. "Asymptotic results for the regression function estimate on continuous time stationary and ergodic data," Statistics & Risk Modeling, De Gruyter, vol. 31(2), pages 1-22, June.
    • Handle: RePEc:bpj:strimo:v:31:y:2014:i:2:p:22:n:1
    DOI: 10.1515/strm-2012-1134
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    References listed on IDEAS

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    1. Laib, Naâmane & Louani, Djamal, 2010. "Nonparametric kernel regression estimation for functional stationary ergodic data: Asymptotic properties," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2266-2281, November.
    2. Castellana, J. V. & Leadbetter, M. R., 1986. "On smoothed probability density estimation for stationary processes," Stochastic Processes and their Applications, Elsevier, vol. 21(2), pages 179-193, February.
    3. Yakowitz, Sidney & Györfi, László & Kieffer, John & Morvai, Gusztáv, 1999. "Strongly Consistent Nonparametric Forecasting and Regression for Stationary Ergodic Sequences," Journal of Multivariate Analysis, Elsevier, vol. 71(1), pages 24-41, October.
    4. Gérard Biau & Kevin Bleakley & László Györfi & György Ottucsák, 2010. "Nonparametric sequential prediction of time series," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(3), pages 297-317.
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