Abstract:
A combination of the method of coupling, Stein technique and the
quasi-convex analysis allowed author to derive unimprovable
inequalities characterizing the distance between a probability
distribution and its zero bias transformation in terms of a wide
class of minimal metrics. In the presentation the basic ideas of
the mentioned approach are explained. Moreover, it is shown how to
obtain optimal estimates of the convergence rate in the Lyapunov
central limit theorem when using ideal probability metrics.
1. И.С.Тюрин (2009), О скорости сходимости в теореме Ляпунова, Теор.
вероят. примен., т. 55, в. 2, 2010, с. 250–270.
2. I.S.Tyurin (2011), Some optimal bounds in CLT using zero biasing,
Stat. and Probab. Letters (в печати).
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