• Journal of the Korean Statistical Society
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• v.24 no.2
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• pp.551-562
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• 1995

We consider the iterated bootstrap method in regression model with heterogeneous error variances. The iterated wild bootstrap confidence intervla of the mean response is considered. It is shown that the iterated wild bootstrap confidence interval has coverage error of order $n^{-1}$ wheresa percentile method interval has an error of order $n^{-1/2}$. The simulation results reveal that the iterated bootstrap method calibrates the coverage error of percentile method interval successfully even for the small sample size.

• Journal of KIISE:Software and Applications
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• v.30 no.3_4
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• pp.251-258
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• 2003

A support vector machine (SVM) is supposed to provide a good generalization performance, but the actual performance of a actually implemented SVM is often far from the theoretically expected level. This is largely because the implementation is based on an approximated algorithm, due to the high complexity of time and space. To improve this limitation, we propose ensemble of SVMs by using Bagging (bootstrap aggregating) and Boosting. By a Bagging stage each individual SVM is trained independently using randomly chosen training samples via a bootstrap technique. By a Boosting stage an individual SVM is trained by choosing training samples according to their probability distribution. The probability distribution is updated by the error of independent classifiers, and the process is iterated. After the training stage, they are aggregated to make a collective decision in several ways, such ai majority voting, the LSE(least squares estimation) -based weighting, and double layer hierarchical combining. The simulation results for IRIS data classification, the hand-written digit recognition and Face detection show that the proposed SVM ensembles greatly outperforms a single SVM in terms of classification accuracy.