Data Analysis with R, Second Edition - Second Edition

Exercises

• One of the great things about the bootstrap is how conceptually simple and flexible the procedure is. This makes it very easy to do our own research on it. In this exercise, we will be doing simulations of simulations. Specifically, to see for ourselves the deterioration of the reliability of bootstrap results as sample sizes get smaller, make samples of a normal distribution of a fixed mean, 30 or 50 times, with sample sizes of 100 to 5, going down by 5 each time. For each of these 30 to 50 times, perform the bootstrap procedure (with a sensible number of replications), and find out which proportion of the time the BCa confidence interval contains the mean we chose. Is it 95%, like we would expect? Repeat the procedure with other ...