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The bootstrap
Author
Tan, Yew Hui
Supervisor
Phang, Rosalind Lay Ping
Abstract
This academic exercise is an introductory study of bootstrap methods on accuracy of point estimates, confidence intervals and hypothesis tests. We first look at the standard error of an estimate and explore three examples, namely the mean, the median and the correlation coefficient. More complicated data structures such as the two-sample problem and regression models are also discussed. In particular, for regression analysis, we investigated briefly two different bootstrapping processes, namely bootstrapping residuals and bootstrapping pairs of data. Another measure of statistical accuracy considered is the bias of an estimate We discussed the bootstrap method for estimating bias and looked into an improved version of this process. On interval estimation, we conducted a simulation study on three types of bootstrap confidence intervals, namely the bootstrap-t interval, the transformed bootstrap-t interval and the percentile interval. An example was given to illustrate the BCa (bias corrected and accelerated) and the ABC (approximate bootstrap confidence) intervals, which are two improved versions of the percentile method. On bootstrap hypothesis testing, we explored on tests concerning a single mean, difference between means and difference between variances. The bootstrap results are compared to those obtained by traditional parametric and non-parametric tests.
Date Issued
1997
Call Number
QA276.8 Tan
Date Submitted
1997