Iterated-Bootstrap Confidence Intervals for the Mean.
NAVAL AEROSPACE MEDICAL RESEARCH LAB PENSACOLA FL
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Several reports indicate that nonparametric bootstrap confidence intervals CIs produced by the percentile method can yield overly liberal Type I error rates in small samples when the nominal alpha level is .05 or less. In the Monte Carlo simulations described here, percentile-method bootstrap 95 CIs for mu produced higher Type I error rates than standard parametric CIs in Gaussian and exponential samples of 40 or fewer observations. Iterated-bootstrap CIs for mu however, yielded Type I error rates near alpha .05 in Gaussian and exponential samples of as few as 10 observations. In exponential samples of 10 or more observations, iterated-bootstrap intervals controlled Type I errors more reliably than parametric intervals and were not obviously inferior to the parametric intervals when the data were Gaussian. Thus, ordinary percentile- method bootstrap CIs for mu may be of questionable accuracy when Type I error rates are to be controlled at values of alpha less than or equal .05 or so. On the other hand, iterated-bootstrap CIs may be preferable to parametric CIs for data that come from a skewed distribution, such as the exponential, provided n is 10 or more. In samples of about 10 observations or more, iterated CIs may yield better Type I error control than parametric CIs when the data are skewed and nearly the same Type I error control when the data are Gaussian. Statistics, Nonparametric statistics, Bootstrap, Confidence intervals.
- Statistics and Probability