Bootstrapping the i.i.d data

Yihui Xie & Lijia Yu 2017-04-04

Use a sunflower scatter plot to illustrate the results of resampling, and a histogram to show the distribution of the statistic of interest.

This is actually a very naive version of bootstrapping but may be useful for novices. By default, the circles denote the original dataset, while the red sunflowers (probably) with leaves denote the points being resampled; the number of leaves just means how many times these points are resampled, as bootstrap samples with replacement. The x-axis is the sample values, and y-axis is the indices of sample points.

The whole process has illustrated the steps of resampling, computing the statistic and plotting its distribution based on bootstrapping.

## bootstrap for 20 random numbers from U(0, 1)
par(mar = c(1.5, 3, 1, 0.1), cex.lab = 0.8, cex.axis = 0.8, mgp = c(2, 0.5, 0), tcl = -0.3)
ani.options(nmax = 50)
## don't want the titles
boot.iid(main = c("", ""))

plot of chunk demo-a

## for the median of 15 points from chi-square(5)
boot.iid(x = rchisq(15, 5), statistic = median, main = c("", ""))

plot of chunk demo-b

## change the layout; or you may try 'mat = matrix(1:2, 1)'
par(mar = c(1.5, 3, 2.5, 0.1), cex.main = 1)
boot.iid(heights = c(1, 2))

plot of chunk demo-c