Statistics 5601 (Geyer, Spring 2006) Examples: Bootstrap Percentile


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Bootstrap Percentile Intervals

Section 13.3 in Efron and Tibshirani.

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Bootstrap Percentile Intervals, Take Two

An alternative method for quantiles preferred by your humble instructor uses the following logic.

Use nboot <- 999 (or some other value such that nboot + 1 is a round number. The reason is that if X(i) is the i-th order statistic from a Uniform(0, 1) distribution

E{X(i)} = i / (n + 1)

Another way to think of this is that the nboot data points divide the number line into nboot + 1 intervals, which as far as we know contain equal probability. They don't contain equal probability because the sample is not the population, but we might as well treat them as such for the purposes of estimation. That is, our nboot data points should be taken as estimators of the quantiles with denominators nboot + 1

In particular, if nboot is 999, then we take the ordered values to be the 0.001, 0.002, . . ., 0.999 quantiles of the sampling distribution of theta.hat. Thus

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