### Name: linear.approx
### Title: Linear Approximation of Bootstrap Replicates
### Aliases: linear.approx
### Keywords: nonparametric

### ** Examples

# Using the city data let us look at the linear approximation to the 
# ratio statistic and its logarithm. We compare these with the 
# corresponding plots for the bigcity data 

ratio <- function(d, w)
     sum(d$x * w)/sum(d$u * w)
city.boot <- boot(city, ratio, R=499, stype="w")
bigcity.boot <- boot(bigcity, ratio, R=499, stype="w")
par(pty="s")
par(mfrow=c(2,2))

# The first plot is for the city data ratio statistic.
city.lin1 <- linear.approx(city.boot)
lim <- range(c(city.boot$t,city.lin1))
plot(city.boot$t, city.lin1, xlim=lim,ylim=lim, 
     main="Ratio; n=10", xlab="t*", ylab="tL*")
abline(0,1)

# Now for the log of the ratio statistic for the city data.
city.lin2 <- linear.approx(city.boot,t0=log(city.boot$t0), 
                           t=log(city.boot$t))
lim <- range(c(log(city.boot$t),city.lin2))
plot(log(city.boot$t), city.lin2, xlim=lim, ylim=lim, 
     main="Log(Ratio); n=10", xlab="t*", ylab="tL*")
abline(0,1)

# The ratio statistic for the bigcity data.
bigcity.lin1 <- linear.approx(bigcity.boot)
lim <- range(c(bigcity.boot$t,bigcity.lin1))
plot(bigcity.lin1,bigcity.boot$t, xlim=lim,ylim=lim,
     main="Ratio; n=49", xlab="t*", ylab="tL*")
abline(0,1)

# Finally the log of the ratio statistic for the bigcity data.
bigcity.lin2 <- linear.approx(bigcity.boot,t0=log(bigcity.boot$t0), 
                              t=log(bigcity.boot$t))
lim <- range(c(log(bigcity.boot$t),bigcity.lin2))
plot(bigcity.lin2,log(bigcity.boot$t), xlim=lim,ylim=lim,
     main="Log(Ratio); n=49", xlab="t*", ylab="tL*")
abline(0,1)

par(mfrow=c(1,1))