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Uniform consistency of a class of regression function estimators for Banach-space valued random variable

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  • Lecoutre, Jean-Pierre

Abstract

This paper deals with an estimator mn of the regression function m(x) = E(Y X = x) with X in the real line and Y in a sufficiently regular Banach space. By using infinite dimensional probability inequalities for sums, we show that mn is uniformly consistent.

Suggested Citation

  • Lecoutre, Jean-Pierre, 1990. "Uniform consistency of a class of regression function estimators for Banach-space valued random variable," Statistics & Probability Letters, Elsevier, vol. 10(2), pages 145-149, July.
    • Handle: RePEc:eee:stapro:v:10:y:1990:i:2:p:145-149
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    Cited by:

    1. Boumahdi, Mounir & Ouassou, Idir & Rachdi, Mustapha, 2023. "Estimation in nonparametric functional-on-functional models with surrogate responses," Journal of Multivariate Analysis, Elsevier, vol. 198(C).
    2. Nengxiang Ling & Lingyu Wang & Philippe Vieu, 2020. "Convergence rate of kernel regression estimation for time series data when both response and covariate are functional," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(6), pages 713-732, August.

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