Exponential bounds via Stein’s method and exchangeable pairs
نویسندگان
چکیده
منابع مشابه
Exponential approximation and Stein’s method of exchangeable pairs
The purpose of this paper is to further develop exponential approximation, using Stein’s method of exchangeable pairs. The first use of exchangeable pairs in exponential approximation was in the paper Chatterjee et al. (2011), which studied the spectrum of the Bernoulli-Laplace Markov chain. Unfortunately the results in Chatterjee et al. (2011), which use the Kolmogorov metric, are very complic...
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This paper derives exponential concentration inequalities and polynomial moment inequalities for the spectral norm of a random matrix. The analysis requires a matrix extension of the scalar concentration theory developed by Sourav Chatterjee using Stein’s method of exchangeable pairs. When applied to a sum of independent random matrices, this approach yields matrix generalizations of the classi...
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Running head: Exponential Approximation by Exchangeable Pairs Version of 4/7/06 By Sourav Chatterjee and Jason Fulman Abstract: A general Berry-Esseen bound is obtained for the exponential distribution using Stein’s method of exchangeable pairs. As an application, an error term is derived for Hora’s result that the spectrum of the Bernoulli-Laplace Markov chain has an exponential limit. This is...
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Stein’s method of exchangeable pairs is examined through five examples in relation to Poisson and normal distribution approximation. In particular, in the case where the exchangeable pair is constructed from a reversible Markov chain, we analyze how modifying the step size of the chain in a natural way affects the error term in the approximation acquired through Stein’s method. It has been note...
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ژورنال
عنوان ژورنال: ScienceAsia
سال: 2018
ISSN: 1513-1874
DOI: 10.2306/scienceasia1513-1874.2018.44.277