International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 45, Pages 2835-2861
doi:10.1155/S0161171203301437

A survey of limit laws for bootstrapped sums

Sándor Csörgő1 and Andrew Rosalsky2

1Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, Szeged H-6720, Hungary
2Department of Statistics, University of Florida, Gainesville 32611, FL, USA

Received 10 January 2003; Revised 27 February 2003

Copyright © 2003 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Concentrating mainly on independent and identically distributed (i.i.d.) real-valued parent sequences, we give an overview of first-order limit theorems available for bootstrapped sample sums for Efron's bootstrap. As a light unifying theme, we expose by elementary means the relationship between corresponding conditional and unconditional bootstrap limit laws. Some open problems are also posed.