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DOI QR Code

CONDITIONAL CENTRAL LIMIT THEOREMS FOR A SEQUENCE OF CONDITIONAL INDEPENDENT RANDOM VARIABLES

  • Yuan, De-Mei ;
  • Wei, Li-Ran ;
  • Lei, Lan
  • Received : 2012.03.01
  • Published : 2014.01.01

Abstract

A conditional version of the classical central limit theorem is derived rigorously by using conditional characteristic functions, and a more general version of conditional central limit theorem for the case of conditionally independent but not necessarily conditionally identically distributed random variables is established. These are done anticipating that the field of conditional limit theory will prove to be of significant applicability.

Keywords

conditional independence;conditional identical distribution;conditional characteristic function;conditional central limit theorem

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