Multivariate normal approximation with Stein’s method of exchangeable pairs under a general linearity condition
نویسندگان
چکیده
منابع مشابه
Random Subgraph Countsand U -statistics: Multivariate Normal Approximation via Exchangeable Pairs and Embedding
In Reinert and Röllin (2009) a new approach—called the ‘embedding method’—was introduced, which allows us tomake use of exchangeable pairs for normal andmultivariate normal approximations with Stein’s method in cases where the corresponding couplings do not satisfy a certain linearity condition. The key idea is to embed the problem into a higher-dimensional space in such a way that the linearit...
متن کاملExponential 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...
متن کاملExponential Approximation by Exchangeable Pairs and Spectral Graph Theory Running head: Exponential Approximation by Exchangeable Pairs
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...
متن کاملExponential approximation by exchangeable pairs and spectral graph theory
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...
متن کاملMultivariate normal approximation using Stein’s method and Malliavin calculus
We combine Stein’s method with Malliavin calculus in order to obtain explicit bounds in the multidimensional normal approximation (in the Wasserstein distance) of functionals of Gaussian fields. Our results generalize and refine the main findings by Peccati and Tudor (2005), Nualart and Ortiz-Latorre (2007), Peccati (2007) and Nourdin and Peccati (2007b, 2008); in particular, they apply to appr...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Annals of Probability
سال: 2009
ISSN: 0091-1798
DOI: 10.1214/09-aop467