Empirical limit theorems for Wiener chaos

Shuyang Bai and Jiemiao Chen

Statistics & Probability Letters, 2024, vol. 215, issue C

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.

Keywords: Limit theorems; Wiener chaos; Multiple stochastic integrals; Empirical measure; Gaussian random measure (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spl.2024.110222

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