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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https://hal.science/hal-02567038
Soumis le : jeudi 7 mai 2020-15:53:47
Dernière modification le : jeudi 28 mars 2024-13:09:58
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- HAL Id : hal-02567038 , version 1
- DOI : 10.1080/10485252.2020.1759597
Citer
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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