Data dependent choice of the tuning parameter for the modified bootstrap

Abstract

It is the purpose of this study to investigate a procedure for estimating the tuning parameter, m, in the modified bootstrap (also known as the m-out-of-n bootstrap, the moon bootstrap or the m/n bootstrap). The procedure which is to be investigated was first proposed by Bickel, Götze and van Zwet (1997). This estimation procedure was then further investigated theoretically by Bickel and Sakov(1999). In order to gain further insight, simulation studies were conducted using this data-based choice of m. The simulations involved constructing 90% confidence upper bounds through the use of the modified bootstrap method of percentile confidence upper bounds, known as the "Hybrid" and "Backwards" bounds. The simulation study provided, among other things, estimates for the coverage probabilities of the procedures. Interesting findings and conclusions of this study are reported.