2024
DOI: 10.3390/math12131996
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Limit Theorems in the Nonparametric Conditional Single-Index U-Processes for Locally Stationary Functional Random Fields under Stochastic Sampling Design

Salim Bouzebda

Abstract: In his work published in (Ann. Probab. 19, No. 2 (1991), 812–825), W. Stute introduced the notion of conditional U-statistics, expanding upon the Nadaraya–Watson estimates used for regression functions. Stute illustrated the pointwise consistency and asymptotic normality of these statistics. Our research extends these concepts to a broader scope, establishing, for the first time, an asymptotic framework for single-index conditional U-statistics applicable to locally stationary random fields {Xs,An:sinRn} obser… Show more

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Cited by 3 publications
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