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Empirical limit theorems for Wiener chaos

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  • Bai, Shuyang
  • Chen, Jiemiao

Abstract

We consider empirical measures in a triangular array setup with underlying distributions varying as sample size grows. We study asymptotic properties of multiple integrals with respect to normalized empirical measures. Limit theorems involving series of multiple Wiener–Itô integrals are established.

Suggested Citation

  • Bai, Shuyang & Chen, Jiemiao, 2024. "Empirical limit theorems for Wiener chaos," Statistics & Probability Letters, Elsevier, vol. 215(C).
    • Handle: RePEc:eee:stapro:v:215:y:2024:i:c:s0167715224001913
    DOI: 10.1016/j.spl.2024.110222
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    References listed on IDEAS

    as
    1. Ivanoff, Gail, 1982. "Central limit theorems for point processes," Stochastic Processes and their Applications, Elsevier, vol. 12(2), pages 171-186, March.
    2. Boistard, Hélène & del Barrio, Eustasio, 2009. "Central limit theorem for multiple integrals with respect to the empirical process," Statistics & Probability Letters, Elsevier, vol. 79(2), pages 188-195, January.
    3. Xichao Sun & Litan Yan, 2017. "Weak convergence to a class of multiple stochastic integrals," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(17), pages 8355-8368, September.
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