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ConditionalU-Statistics for Dependent Random Variables

Author

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  • Harel, Michel
  • Puri, Madan L.

Abstract

W. Stute (Ann. Probab.19,No. 2 (1991), 812-825) introduced a class of so-calledU-statistics, which may be viewed as a generalization of the Nadaraya-Watson estimates of a regression function. In this paper, we extend the results from the independent case to the dependent case.

Suggested Citation

  • Harel, Michel & Puri, Madan L., 1996. "ConditionalU-Statistics for Dependent Random Variables," Journal of Multivariate Analysis, Elsevier, vol. 57(1), pages 84-100, April.
    • Handle: RePEc:eee:jmvana:v:57:y:1996:i:1:p:84-100
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    Citations

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    Cited by:

    1. Salim Bouzebda & Amel Nezzal & Tarek Zari, 2022. "Uniform Consistency for Functional Conditional U -Statistics Using Delta-Sequences," Mathematics, MDPI, vol. 11(1), pages 1-39, December.
    2. Salim Bouzebda & Thouria El-hadjali & Anouar Abdeldjaoued Ferfache, 2023. "Uniform in Bandwidth Consistency of Conditional U-statistics Adaptive to Intrinsic Dimension in Presence of Censored Data," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(2), pages 1548-1606, August.
    3. Salim Bouzebda & Inass Soukarieh, 2022. "Non-Parametric Conditional U -Processes for Locally Stationary Functional Random Fields under Stochastic Sampling Design," Mathematics, MDPI, vol. 11(1), pages 1-69, December.
    4. Salim Bouzebda, 2024. "Limit Theorems in the Nonparametric Conditional Single-Index U -Processes for Locally Stationary Functional Random Fields under Stochastic Sampling Design," Mathematics, MDPI, vol. 12(13), pages 1-81, June.
    5. Michel Harel & Madan Puri, 2004. "Universally consistent conditionalU-statistics for absolutely regular processes and its applications for hidden Markov models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 56(4), pages 819-832, December.
    6. Terpstra, Jeffrey T. & Rao, M. Bhaskara, 2002. "On the asymptotic distribution of a multivariate GR-estimate for a VAR(p) time series," Statistics & Probability Letters, Elsevier, vol. 60(2), pages 219-230, November.
    7. Salim Bouzebda & Boutheina Nemouchi, 2023. "Weak-convergence of empirical conditional processes and conditional U-processes involving functional mixing data," Statistical Inference for Stochastic Processes, Springer, vol. 26(1), pages 33-88, April.

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