Statistica Sinica 11(2001), 1-21

BOOTSTRAP METHODS FOR THE UP AND DOWN TEST

ON PYROTECHNICS SENSITIVITY ANALYSIS

M. T. Chao and C. D. Fuh

Academia Sinica

Abstract: We start with a data set recently obtained from a Bruceton test. The data come from the study of CS-M-3 ignitor in a military experiment and are analyzed by the up-and-down method of Dixon and Mood (1948). We reexamine the method and develop a more appropriate inference that takes account of the special dependent data structure. Two bootstrap confidence interval procedures, percentile and bootstrap-$t$, are introduced to find approximate confidence intervals for the parameters of interest. A simulation study shows that the bootstrap-$t$, with proper bias corrections, gives better coverage probability, but is considerably more computer-intensive than non-bias-corrected versions. This leads to the development of an importance resampling technique which can reduce the CPU time by a factor of 10 or more. Finally, we apply the proposed procedure to analyze our data set.

Key words and phrases: Bootstrap, importance resampling, Markov chains, maximum likelihood estimate, probit model, sequential design, up and down method.