Open AccessA New General Estimate of the Rate of Convergence in the Central Limit Theorem in R k
Author(s) -
В. В. Сазонов
Publication year - 1974
Publication title -
proceedings of the national academy of sciences of the united states of america
Language(s) - English
Resource type - Journals
eISSN - 1091-6490
pISSN - 0027-8424
DOI - 10.1073/pnas.71.1.118
Subject(s) - central limit theorem , mathematics , independent and identically distributed random variables , moment (physics) , limit (mathematics) , convergence (economics) , rate of convergence , boundary (topology) , regular polygon , distribution (mathematics) , mathematical analysis , type (biology) , convex set , combinatorics , convex optimization , random variable , statistics , geometry , physics , ecology , channel (broadcasting) , engineering , classical mechanics , electrical engineering , economics , biology , economic growth
A general theorem is proved which gives an estimate of the rate of convergence on convex sets in the multidimensional central limit theorem for identically distributed summands. The estimate depends on the distance of the boundary of the convex set from the origin (the larger the distance, the better the estimate). The estimate makes sense under minimal requirements on the moments. Furthermore, the dependence on the distribution of a summand in it is in terms of pseudo-moment type quantities which may be small even if the moments are large.