21 Bootstrapping Regression Models - SAGE Publications …

21 BootstrappingRegressionModelsBootstrappi ngis a nonparametric approach to statistical inference that substitutes computationfor more traditional distributional assumptions and asymptotic offersa number of advantages: The bootstrap is quite general, although there are some cases in which it fails. Because it does not require distributional assumptions (such as normally distributed errors),the bootstrap can provide more accurate inferences when the data are not well behaved orwhen the sample size is small. It is possible to apply the bootstrap to statistics with sampling distributions that are difficultto derive, even asymptotically. It is relatively simple to apply the bootstrap to complex data-collection plans (such asstratified and clustered samples). Bootstrapping BasicsMy principal aim is to explain how to bootstrap Regression Models (broadly construed to includegeneralized linear Models , etc.)

The mean of the 256 bootstrap sample means is just the original sample mean, Y = 2.75. The standard deviation of the bootstrap means is SD∗(Y∗) = nn b=1(Y ∗ b −Y)2 nn = 1.745 We divide here by nn rather than by nn −1 because the distribution of the nn = 256 bootstrap sample means (Figure 21.1) is known, not estimated. The standard ...

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