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• W3201419613 abstract "In the seventies, Charles Stein revolutionized the way of proving the central limit theorem by introducing a method that utilizes a characterization equation for Gaussian distribution. In the last 50 years, much research has been done to adapt and strengthen this method to a variety of different settings and other limiting distributions. However, it has not been yet extended to study conditional convergences. In this article we develop a novel approach, using Stein’s method for exchangeable pairs, to find a rate of convergence in the conditional central limit theorem of the form (Xn∣Yn=k), where (Xn,Yn) are asymptotically jointly Gaussian, and extend this result to a multivariate version. We apply our general result to several concrete examples, including pattern count in a random binary sequence and subgraph count in Erdős–Rényi random graph." @default.
• W3201419613 created "2021-09-27" @default.
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• W3201419613 date "2023-03-01" @default.
• W3201419613 modified "2023-09-23" @default.
• W3201419613 title "Stein’s method for conditional central limit theorem" @default.
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• W3201419613 doi "https://doi.org/10.1214/22-aop1613" @default.
• W3201419613 hasPublicationYear "2023" @default.
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