Symbolic computation of nonparametric bootstrap estimators and their properties

grantor: University of TorontoThe bootstrap was introduced in 1979 as a computer-intensive method for estimating the standard error and other properties of an estimator. This thesis focuses on how the same objective can be achieved, in many cases, by the development and implementation of computer algorithms for the symbolic computation and evaluation of series expansions. The analytic bootstrap permits the calculation of standard errors for a wide variety of estimators in a fraction of the time and with comparable or better accuracy when compared with conventional bootstrap Monte Carlo resampling. In addition, properties such as bias and variance of bootstrap estimators may be assessed. The methodology is applied to examples from Efron and Tibshirani (1993) involving the correlation coefficient, the Behrens-Fisher statistic, double-bootstrapping and $BC\sb{a}$ bootstrap confidence intervals. An alternative methodology based on the exhaustive enumeration of bootstrap resamples is also presented and illustrated for the case of the median. Implications for future work are discussed.Ph.D