Abstract
We use Poincare-type inequalities to prove the sufficiency and necessity of the Lindeberg condition in the central limit theorem.
Citation
Louis H. Y. Chen. "The Central Limit Theorem and Poincare-Type Inequalities." Ann. Probab. 16 (1) 300 - 304, January, 1988. https://doi.org/10.1214/aop/1176991902
Information
Published: January, 1988
First available in Project Euclid: 19 April 2007
zbMATH: 0646.60029
MathSciNet: MR920272
Digital Object Identifier: 10.1214/aop/1176991902
Subjects:
Primary:
60F05
Secondary:
26D10
,
60E15
Keywords:
central limit theorem
,
characterization of the normal distribution
,
Poincare-type inequalities
Rights: Copyright © 1988 Institute of Mathematical Statistics
