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

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.