Small Sampie Properties of Nonparametric Bootstrap t Confidence intervals

Abstract

Confidence interval construction for central tendency is a problem of practical consequence for those who must analyze air contaminant data. Determination of compliance with relevant ambient air quality criteria and assessment of associated health risks depend upon quantifying the uncertainty of estimated mean pollutant concentrations. The bootstrap is a resampling technique that has been steadily gaining popularity and acceptance during the past several years. A potentially powerful application of the bootstrap is the construction of confidence intervals for any parameter of any underlying distribution. Properties of bootstrap confidence intervals were determined for samples generated from lognormal, gamma, and Weibull distributions. Bootstrap t intervals, while having smaller coverage errors than Student's t or other bootstrap methods, under-cover for small samples from skewed distributions. Therefore, we caution against using the bootstrap to construct confidence intervals for the mean without first considering the effects of sample size and skew. When sample sizes are small, one might consider using the median as an estimate of central tendency. Confidence intervals for the median are easy to construct and do not under-cover. Data collected by the Northeast States for Coordinated Air Use Management (NESCAUM) are used to illustrate application of the methods discussed.