The example done by the percentile method
done by the bootstrap t method, what DeGroot and Schervish call
the percentile-t method
.
We use interquartile range, calculated by the IQR function
as a robust estimator of scale. The hopefully asymptotically pivotal
quantity on which our bootstrap is based is
mean(x, trim = 0.2) - θ) / IQR(x)
which of course has the bootstrap analog
mean(x.star, trim = 0.2) - theta.hat) / IQR(x.star)
| Bootstrap percentile interval | (−0.2395333, 0.2025333) |
| Bootstrap t interval | (−0.215350, 0.207294) |
Not very different here. These methods do behave quite differently when the distribution of the estimator is highly skewed.