Bootstrap Resampling

Abstract

The bootstrap is a resampling method for statistical inference. It is commonly used to estimate confidence intervals, but it can also be used to estimate bias and variance of an estimator or calibrate hypothesis tests. Papers that illustrate the diversity of recent environmetric applications of the bootstrap can be found in toxicology [2], fisheries surveys [31], groundwater and air pollution modeling [1, 4], chemometrics [35], hydrology [14], phylogenetics [23], spatial point patterns [33], ecological indices [9], and multivariate summarization [24, 38]. The literature on the bootstrap is extensive. Booklength treatments of the concepts, applications, and theory of the bootstrap range in content from those that emphasize applications [19], to comprehensive treatments [3, 5, 13], to those that emphasize theory [11, 15, 18, 28]. Major review articles on the bootstrap and its applications include [7], [8], [12] and [37]. Articles describing the bootstrap and demonstrating its use to nonstatisticians have been published in many different journals. Extensive bibliographies, listing applications, are included in [3] and [19]. This entry cannot duplicate the comprehensive coverage found in these books and articles. Instead, I will illustrate bootstrap concepts using a simple example, describe different types of bootstraps and some of their theoretical and practical properties, discuss computation and other details, and indicate extensions that are especially appropriate for environmetric data. The methods will be illustrated using data on heavy metal concentrations in groundwater [22] and magnesium concentration in blood.