Convergence determining sets in the central limit theorem

✍ Scribed by Peter Hall; J. C. H. Wightwick

• Publisher: Springer
• Year: 1986
• Tongue: English
• Weight: 707 KB
• Volume: 71
• Category: Article
• ISSN: 1432-2064
• DOI: 10.1007/bf00366269

✦ Synopsis

A complete characterisation is given of the class of all doublets which determine the rate of convergence in the central limit theorem. This enables a number of important properties of convergence determining sets to be deduced. In particular, it is shown that no singleton can be convergence determining, and any set consisting of four or more distinct points is convergence determining. Numerical and analytic methods are used to derive the geometry of the class of all convergence determining doublets.