ABSTRACT
The goal of Chapter 14 is to introduce the use of both nonparametric and parametric bootstrap methods for characterizing sampling errors of statistics. First, the concept of train-test validation is discussed, and then this is followed by a discussion of K-fold cross-validation. Next bootstrap methods are introduced. The essential idea of the nonparametric bootstrap is to sample with replacement from a set of n data records n times to generate a bootstrap data set. This procedure is then repeated m times to obtain m bootstrap data sets each consisting of n records. Statistics such the average prediction error and its sampling error are then estimated by computing the average and standard deviation of m prediction errors for the m bootstrap data sets. The parametric bootstrap is essentially the same as the nonparametric bootstrap except bootstrap data sets are generated by sampling with replacement from a probability model with a known parameter vector. Applications of these methods for estimating standard errors of parameter estimates, detecting model misspecification, comparing competing models with respect to a single statistical environment, and examining conditions for parameter invariance across different statistical environments are discussed.
