Transcription of 21 Bootstrapping Regression Models
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21 Bootstrapping Regression Models
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.), but the topic is best introduced in a simpler context: Supposethat we draw an independent random sample from a large concreteness andsimplicity, imagine that we sample four working, married couples, determining in each case thehusband s and wife s income, as recorded in Table I will focus on the difference in incomesbetween husbands and wives, denoted asYifor theith want to estimate the mean difference in income between husbands and wives in the pop-ulation.
588 Chapter 21. Bootstrapping Regression Models Table 21.1 Contrived “Sample” of Four Married Couples, Showing Husbands’ and Wives’ Incomes in Thousands of Dollars Observation Husband’s Income Wife’s Income Difference Yi 124 18 6
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