```
op <- options(digits = 5)
# Usual bootstrap of the ratio of means using the city data
ratio <- function(d, w) sum(d$x * w)/sum(d$u * w)
boot(city, ratio, R = 999, stype = "w")
# Stratified resampling for the difference of means. In this
# example we will look at the difference of means between the final
# two series in the gravity data.
diff.means <- function(d, f)
{ n <- nrow(d)
gp1 <- 1:table(as.numeric(d$series))[1]
m1 <- sum(d[gp1,1] * f[gp1])/sum(f[gp1])
m2 <- sum(d[-gp1,1] * f[-gp1])/sum(f[-gp1])
ss1 <- sum(d[gp1,1]^2 * f[gp1]) - (m1 * m1 * sum(f[gp1]))
ss2 <- sum(d[-gp1,1]^2 * f[-gp1]) - (m2 * m2 * sum(f[-gp1]))
c(m1 - m2, (ss1 + ss2)/(sum(f) - 2))
}
grav1 <- gravity[as.numeric(gravity[,2]) >= 7,]
boot(grav1, diff.means, R = 999, stype = "f", strata = grav1[,2])
# In this example we show the use of boot in a prediction from
# regression based on the nuclear data. This example is taken
# from Example 6.8 of Davison and Hinkley (1997). Notice also
# that two extra arguments to 'statistic' are passed through boot.
nuke <- nuclear[, c(1, 2, 5, 7, 8, 10, 11)]
nuke.lm <- glm(log(cost) ~ date+log(cap)+ne+ct+log(cum.n)+pt, data = nuke)
nuke.diag <- glm.diag(nuke.lm)
nuke.res <- nuke.diag$res * nuke.diag$sd
nuke.res <- nuke.res - mean(nuke.res)
# We set up a new data frame with the data, the standardized
# residuals and the fitted values for use in the bootstrap.
nuke.data <- data.frame(nuke, resid = nuke.res, fit = fitted(nuke.lm))
# Now we want a prediction of plant number 32 but at date 73.00
new.data <- data.frame(cost = 1, date = 73.00, cap = 886, ne = 0,
ct = 0, cum.n = 11, pt = 1)
new.fit <- predict(nuke.lm, new.data)
nuke.fun <- function(dat, inds, i.pred, fit.pred, x.pred)
{
lm.b <- glm(fit+resid[inds] ~ date+log(cap)+ne+ct+log(cum.n)+pt,
data = dat)
pred.b <- predict(lm.b, x.pred)
c(coef(lm.b), pred.b - (fit.pred + dat$resid[i.pred]))
}
nuke.boot <- boot(nuke.data, nuke.fun, R = 999, m = 1,
fit.pred = new.fit, x.pred = new.data)
# The bootstrap prediction squared error would then be found by
mean(nuke.boot$t[, 8]^2)
# Basic bootstrap prediction limits would be
new.fit - sort(nuke.boot$t[, 8])[c(975, 25)]
# Finally a parametric bootstrap. For this example we shall look
# at the air-conditioning data. In this example our aim is to test
# the hypothesis that the true value of the index is 1 (i.e. that
# the data come from an exponential distribution) against the
# alternative that the data come from a gamma distribution with
# index not equal to 1.
air.fun <- function(data) {
ybar <- mean(data$hours)
para <- c(log(ybar), mean(log(data$hours)))
ll <- function(k) {
if (k <= 0) 1e200 else lgamma(k)-k*(log(k)-1-para[1]+para[2])
}
khat <- nlm(ll, ybar^2/var(data$hours))$estimate
c(ybar, khat)
}
air.rg <- function(data, mle) {
# Function to generate random exponential variates.
# mle will contain the mean of the original data
out <- data
out$hours <- rexp(nrow(out), 1/mle)
out
}
air.boot <- boot(aircondit, air.fun, R = 999, sim = "parametric",
ran.gen = air.rg, mle = mean(aircondit$hours))
# The bootstrap p-value can then be approximated by
sum(abs(air.boot$t[,2]-1) > abs(air.boot$t0[2]-1))/(1+air.boot$R)
options(op)
```

Run the code above in your browser using DataLab