Lower bounds for the rate of convergence in the central limit theorem in Banach spaces

1986 ◽  
Vol 25 (4) ◽  
pp. 312-320 ◽  
Author(s):  
V. Bentkus
Author(s):  
Peter Hall ◽  
T. Nakata

AbstractThe leading term approach to rates of convergence is employed to derive non-uniform and global descriptions of the rate of convergence in the central limit theorem. Both upper and lower bounds are obtained, being of the same order of magnitude, modulo terms of order n-r. We are able to derive general results by considering only those expansions with an odd number of terms.


1981 ◽  
Vol 89 (3) ◽  
pp. 511-523 ◽  
Author(s):  
Peter Hall

AbstractWe obtain upper and lower bounds of the same order of magnitude for the error between the distribution of a sum of independent and identically distributed random variables, and a normal approximation by a portion of a Chebychev-Cramér series. Our results are sufficiently general to contain the familiar characterizations by Ibragimov(4), Heyde and Leslie (3) and Lifshits(5), and complement some of those obtained earlier by the author (2).


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