Normal approximation for nonlinear statistics using a concentration inequality approach

By Louis H. Y. Chen, Qi-Man Shao. 2007

75 citations recorded by the source corpus.

Let T be a general sampling statistic that can be written as a linear statistic plus an error term. Uniform and non-uniform Berry-Esseen type bounds for T are obtained. The bounds are best possible for many known statistics. Applications to U-statistic, multi-sample U-statistic, L-statistic, random sums, and functions of non-linear statistics are discussed.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/3a5f251451e7cd23f2c560d356f01720e040fe06

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In Artificial Intelligence

In Statistics and Probability

Citations in the corpus

Stein's method for normal approximation (2005, methodology): “The approach has further been shown to be effective in obtaining not only uniform but also non-uniform Berry–Esseen bounds for the accuracy of normal approximation for independent random variables (Chen & Shao, 2001) and for locally dependent random fields as well (Chen & Shao, 2004a).”
Bootstrapping and sample splitting for high-dimensional, assumption-lean inference (2016, background): “(2016); Chen and Shao (2007); Anastasiou and Reinert (2014); Anastasiou and Ley (2015); Anastasiou and Gaunt (2016). Our results are in the same spirit but we keep careful track of the effect of dimension and the eigenvalues of Σ, while leveraging results from Chernozhukov et al.”
Optimal-order bounds on the rate of convergence to normality in the multivariate delta method (2009, methodology): “1)), in a combination with the Stein-type concentration method developed by Chen and Shao [11].”