Bootstrap methods for confidence intervals of percentiles from dataset containing nondetected observations using lognormal distribution

Abstract

AbstractWe evaluated 12 types of bootstrap methods for estimating the confidence intervals of percentiles predicted from a dataset containing nondetected (ND) results of Monte Carlo simulation. The bootstrap prediction process, which computes the confidence intervals, comprises three steps: resampling, calculating bootstrap parameters and computing confidence intervals. We selected several methods—parametric or nonparametric methods for resampling, lognormal or truncated lognormal for parent distribution, and ‘percentile’, ‘bootstrap‐t’ or ‘BCa’ methods for computing the confidence intervals. The reliabilities of these bootstrap methods were compared. In addition, we used environmental monitoring data, which were obtained in 2002 from various rivers in Japan for the verification of the bootstrap methods. The bootstrap confidence intervals for the five proposed methods were compared from the viewpoint of reliability. Based on the results computed by the ‘lognormal, parametric, bootstrap‐t’ method (LN‐P‐Bt)—the most reliable method—95% of the upper confidence limits of the 95th percentiles were from 1.7 to 2.1 times greater than the 95th percentiles directly predicted from the actual sample, and the logarithmic ranges for 90% of the bootstrap confidence intervals varied from 3.0 to 4.4. With regard to the maximum value among the five applied methods, the 95% upper confidence limits of the 95th percentiles were from 3.5 to 7.0 times greater than the 95th percentiles. The parent distribution cannot be assumed to randomly conform to a parametric distribution function particularly in the case of environmental monitoring data. For the conservative estimates, the confidence limits should be comprehensively evaluated from the values estimated by several methods that are established on the basis of different assumptions. Copyright © 2006 John Wiley & Sons, Ltd.