Rate of Convergence in the Central Limit Theorem for Fields of Associated Random Variables

1996 ◽  
Vol 40 (1) ◽  
pp. 136-144 ◽  
Author(s):  
A. V. Bulinskii
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Rate Of Convergence ◽  
Central Limit ◽  
Random Variables ◽  
Associated Random Variables ◽  
The Central Limit Theorem

Characterizing the rate of convergence in the central limit theorem. II

1981 ◽  
Vol 89 (3) ◽  
pp. 511-523 ◽  
Author(s):  
Peter Hall
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Rate Of Convergence ◽  
Central Limit ◽  
Lower Bounds ◽  
Normal Approximation ◽  
Random Variables ◽  
Upper And Lower Bounds ◽  
The Central Limit Theorem ◽  
Order Of Magnitude

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).

scholarly journals Central limit theorem for linear processes generated by IID random variables under the sub-linear expectation

2021 ◽  
Vol 36 (2) ◽  
pp. 243-255
Author(s):  
Wei Liu ◽  
Yong Zhang
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Invariance Principle ◽  
Random Variables ◽  
Probability Measures ◽  
Linear Processes ◽  
The Central Limit Theorem

AbstractIn this paper, we investigate the central limit theorem and the invariance principle for linear processes generated by a new notion of independently and identically distributed (IID) random variables for sub-linear expectations initiated by Peng [19]. It turns out that these theorems are natural and fairly neat extensions of the classical Kolmogorov’s central limit theorem and invariance principle to the case where probability measures are no longer additive.

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