Statistica Sinica 10(2000), 475-496

NONPARAMETRIC CONFIDENCE INTERVALS BASED ON

EXTREME BOOTSTRAP PERCENTILES

Stephen M. S. Lee

The University of Hong Kong

Abstract: Monte Carlo approximation of standard bootstrap confidence intervals relies on the drawing of a large number, say, of bootstrap resamples. Conventional choice of is often made on the order of 1,000. While this choice may prove to be more than sufficient for some cases, it may be far from adequate for others. A new approach is suggested to construct confidence intervals based on extreme bootstrap percentiles and an adaptive choice of . It economizes on the computational effort in a problem-specific fashion, yielding stable confidence intervals of satisfactory coverage accuracy.

Key words and phrases: Bootstrap, confidence limit, coverage, Edgeworth expansion, equi-tailed, extreme percentile, Monte Carlo, noncoverage, smooth function model.