Convexity and Concentration by Eric Carlen Mokshay Madiman & Elisabeth M. Werner

Author:Eric Carlen, Mokshay Madiman & Elisabeth M. Werner
Language: eng
Format: epub
Publisher: Springer New York, New York, NY

Sergey G. Bobkov

Email: [email protected]

Abstract

This is mostly a review of results and proofs related to asymptotic expansions for characteristic functions of sums of independent random variables (known also as Edgeworth-type expansions). A number of known results is refined in terms of Lyapunov coefficients of non-integer orders.

Let X 1, …, X n be independent random variables with zero means, variances σ k 2 = Var(X k ), such that ∑ k = 1 n σ k 2 = 1, and with finite absolute moments of some integer order s ≥ 2. Introduce the Lyapunov coefficients

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