# usual bootstrap of the ratio of means using the city data
data(city)
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.
data(gravity)
diff.means <- function(d, f)
{ n <- nrow(d)
gp1 <- 1:table(as.numeric(d$series))[1]
m1 <- sum(d[gp1,1] * f[gp1])/sum(f[gp1])
m2 <- sum(d[-gp1,1] * f[-gp1])/sum(f[-gp1])
ss1 <- sum(d[gp1,1]^2 * f[gp1]) -
(m1 * m1 * sum(f[gp1]))
ss2 <- sum(d[-gp1,1]^2 * f[-gp1]) -
(m2 * m2 * sum(f[-gp1]))
c(m1-m2, (ss1+ss2)/(sum(f)-2))
}
grav1 <- gravity[as.numeric(gravity[,2])>=7,]
boot(grav1, diff.means, R=999, stype="f", strata=grav1[,2])
# In this example we show the use of boot in a prediction from
# regression based on the nuclear data. This example is taken
# from Example 6.8 of Davison and Hinkley (1997). Notice also
# that two extra arguments to statistic are passed through boot.
data(nuclear)
nuke <- nuclear[,c(1,2,5,7,8,10,11)]
nuke.lm <- glm(log(cost)~date+log(cap)+ne+ ct+log(cum.n)+pt, data=nuke)
nuke.diag <- glm.diag(nuke.lm)
nuke.res <- nuke.diag$res*nuke.diag$sd
nuke.res <- nuke.res-mean(nuke.res)
# We set up a new dataframe with the data, the standardized
# residuals and the fitted values for use in the bootstrap.
nuke.data <- data.frame(nuke,resid=nuke.res,fit=fitted(nuke.lm))
# Now we want a prediction of plant number 32 but at date 73.00
new.data <- data.frame(cost=1, date=73.00, cap=886, ne=0,
ct=0, cum.n=11, pt=1)
new.fit <- predict(nuke.lm, new.data)
nuke.fun <- function(dat, inds, i.pred, fit.pred, x.pred)
{
assign(".inds", inds, envir=.GlobalEnv)
lm.b <- glm(fit+resid[.inds] ~date+log(cap)+ne+ct+
log(cum.n)+pt, data=dat)
pred.b <- predict(lm.b,x.pred)
remove(".inds", envir=.GlobalEnv)
c(coef(lm.b), pred.b-(fit.pred+dat$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 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) out <- 1e200 # not NA
else out <- lgamma(k)-k*(log(k)-1-para[1]+para[2])
out
}
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$hours <- rexp(nrow(out), 1/mle)
out
}
data(aircondit)
air.boot <- boot(aircondit, air.fun, R=999, sim="parametric",
ran.gen=air.rg, mle=mean(aircondit$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)Run the code above in your browser using DataLab