A square bias transformation: properties and applications
Abstract
The properties of the square bias transformation are studied, in particular, the precise momenttype estimate for the $L_1$metric between the transformed and the original distributions is proved, a relation between their characteristic functions is found. As a corollary, some new momenttype estimates for the proximity of arbitrary characteristic function with zero mean and finite third moment to the normal one with zero mean and the same variance are proved involving the double integrals of the square and zero bias transformations.
 Publication:

arXiv eprints
 Pub Date:
 December 2012
 DOI:
 10.48550/arXiv.1212.6775
 arXiv:
 arXiv:1212.6775
 Bibcode:
 2012arXiv1212.6775S
 Keywords:

 Mathematics  Probability;
 60E10;
 60E15
 EPrint:
 11 pages. The proof of the main theorem has been simplified