Limit theorems for a class of processes generalizing the
            <i>U</i>
            -empirical process

Bouzebda, Salim; Soukarieh, Inass

doi:10.1080/17442508.2024.2320402

Stochastics

2024

DOI: 10.1080/17442508.2024.2320402

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Limit theorems for a class of processes generalizing the U -empirical process

Salim Bouzebda,

Inass Soukarieh

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2024

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Cited by 3 publications

References 99 publications

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Asymptotics for non-degenerate multivariate U-statistics with estimated nuisance parameters under the null and local alternative hypotheses

Desgagné,

Genest,

Ouimet

2024

Journal of Multivariate Analysis

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Asymptotics for non-degenerate multivariate U-statistics with estimated nuisance parameters under the null and local alternative hypotheses

Desgagné,

Genest,

Ouimet

2024

Journal of Multivariate Analysis

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Oracle inequalities and upper bounds for kernel conditional U-statistics estimators on manifolds and more general metric spaces associated with operators

Bouzebda,

Taachouche

2024

Stochastics

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Weak convergence of the conditional single index $ U $-statistics for locally stationary functional time series

Bouzebda

2024

MATH

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<abstract><p>In recent years, there has been a notable shift in focus towards the analysis of non-stationary time series, driven largely by the complexities associated with delineating significant asymptotic behaviors inherent to such processes. The genesis of the theory of locally stationary processes arises from the quest for asymptotic inference grounded in nonparametric statistics. This paper endeavors to formulate a comprehensive framework for conducting inference within the realm of locally stationary functional time series by harnessing the conditional $ U $-statistics methodology as propounded by W. Stute in 1991. The proposed methodology extends the Nadaraya-Watson regression function estimations. Within this context, a novel estimator was introduced for the single index conditional $ U $-statistics operator, adept at accommodating the non-stationary attributes inherent to the data-generating process. The primary objective of this paper was to establish the weak convergence of conditional $ U $-processes within the domain of locally stationary functional mixing data. Specifically, the investigation delved into scenarios of weak convergence involving functional explanatory variables, considering both bounded and unbounded sets of functions while adhering to specific moment requirements. The derived findings emanate from broad structural specifications applicable to the class of functions and models under scrutiny. The theoretical insights expounded in this study constitute pivotal tools for advancing the domain of functional data analysis.</p></abstract>

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Limit theorems for a class of processes generalizing the U -empirical process

Cited by 3 publications

References 99 publications

Asymptotics for non-degenerate multivariate U-statistics with estimated nuisance parameters under the null and local alternative hypotheses

Asymptotics for non-degenerate multivariate U-statistics with estimated nuisance parameters under the null and local alternative hypotheses

Oracle inequalities and upper bounds for kernel conditional U-statistics estimators on manifolds and more general metric spaces associated with operators

Weak convergence of the conditional single index $ U $-statistics for locally stationary functional time series

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