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Article Dans Une Revue Journal of Nonparametric Statistics Année : 2020

Uniform consistency and uniform in bandwidth consistency for nonparametric regression estimates and conditional U-statistics involving functional data

Résumé

W. Stute [(1991), Annals of Probability, 19, 812–825] introduced a class of so-called conditional U-statistics, which may be viewed as a generalisation of the Nadaraya–Watson estimates of a regression function. Stute proved their strong pointwise consistency to m(t):=E[ϕ(Y1,…,Ym)∣∣(X1,…,Xm)=t],for t∈Rdm. We apply the methods developed in Dony and Mason [(2008), Bernoulli, 14(4), 1108–1133] to establish uniformity in t and in bandwidth consistency (i.e. hn , hn∈[an,bn] where 0
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Dates et versions

hal-02567038 , version 1 (07-05-2020)

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Salim Bouzebda, Boutheina Nemouchi. Uniform consistency and uniform in bandwidth consistency for nonparametric regression estimates and conditional U-statistics involving functional data. Journal of Nonparametric Statistics, 2020, 32 (2), pp.452-509. ⟨10.1080/10485252.2020.1759597⟩. ⟨hal-02567038⟩
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