Berry-Esseen bounds for studentized statistics by Steins method

Author/s: Dave Bradfield, PhD
Availability: Open Access
Type: Thesis
Year: 2012

Abstract: The Steins method, originally introduced by Stein (1972), gives us a novel wayto investigate normal approximation. This method has since been developed in different areas and can be applied to different distributional approximations. It is a very powerful tool to estimate the absolute error of approximations and also the relative error. In this thesis, we establish the uniform and non-uniform Berry-Esseen bound for a class of Studentized statistics via Steins method. In particular, we recover the optimal results for Students t-statistics, Studentized U-statistics and Studentized L-statistics.

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