Properties of Bootstrap Samples

SYNOPTIC ABSTRACT

Efron'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.

Key Words and Phrases:

• bootstrap
• cross-validation
• classical occupancy problem
• discriminant analysis
• misclassification probability
• urn models