Properties of Bootstrap Samples

SYNOPTIC ABSTRACTEfron's version of the “bootstrap” procedure was devised as a method for obtaining nonparametric estimates of Standard deviations and biases of estimators. Important applications include error rate of classifiers, non-linear regression, econometric modeling, discriminant analysis and principal components. Applications of the bootstrap procedure usually require the generation of “bootstrap samples.” This paper presents a connection between bootstrap samples and the classical occupancy problem. Small sample properties of a bootstrap sample are obtained based on the application of results on the occupancy problem. The implications of these results on the estimate of misclassification probability in discriminant analysis are addressed.