Normal approximation for nonlinear statistics using a concentration inequality approach

Details Normal approximation for nonlinear statistics using a concentration inequality approach Normal approximation for nonlinear statistics using a concentration inequality approach

2007-08-31

arxiv.org/abs/0708.4272v1

Bernoulli 2007, Vol. 13, No. 2, 581-599

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.3150/07-BEJ5164 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statist

Scientific paper

10.3150/07-BEJ5164

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 the best possible for many known
statistics. Applications to U-statistics, multisample U-statistics,
L-statistics, random sums and functions of nonlinear statistics are discussed.

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