A Non-Uniform Estimate for the Speed of Convergence in the Central Limit Theorem in R

1977 ◽  
Vol 21 (2) ◽  
pp. 270-282 ◽  
Author(s):  
V. V. Ul’yanov
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Uniform Estimate ◽  
Speed Of Convergence ◽  
The Central Limit Theorem

scholarly journals On Feller's criterion for the law of the iterated logarithm

1994 ◽  
Vol 17 (2) ◽  
pp. 323-340 ◽  
Author(s):  
Deli Li ◽  
M. Bhaskara Rao ◽  
Xiangchen Wang
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Uniform Estimate ◽  
Random Variables ◽  
Independent Random Variables ◽  
Partial Sums ◽  
The Central Limit Theorem ◽  
Iterated Logarithm ◽  
The Law

Combining Feller's criterion with a non-uniform estimate result in the context of the Central Limit Theorem for partial sums of independent random variables, we obtain several results on the Law of the Iterated Logarithm. Two of these results refine corresponding results of Wittmann (1985) and Egorov (1971). In addition, these results are compared with the corresponding results of Teicher (1974), Tomkins (1983) and Tomkins (1990)

scholarly journals A uniform estimate for the rate of convergence in the multidimensional central limit theorem for homogeneous Markov chains

1996 ◽  
Vol 19 (3) ◽  
pp. 441-450
Author(s):  
M. Gharib
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Rate Of Convergence ◽  
Central Limit ◽  
Remainder Term ◽  
Transition Probabilities ◽  
Uniform Estimate ◽  
Homogeneous Markov Chain ◽  
The Central Limit Theorem ◽  
Third Moment

In this paper a uniform estimate is obtained for the remainder term in the central limit theorem (CLT) for a sequence of random vectors forming a homogeneous Markov chain with arbitrary set of states. The result makes it possible to estimate the rate of convergence in the CLT without assuming the finiteness of the absolute third moment of the transition probabilities. Some consequences are also proved.

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