linear.approx {boot}  R Documentation 
Linear Approximation of Bootstrap Replicates
Description
This function takes a bootstrap object and for each bootstrap replicate it calculates the linear approximation to the statistic of interest for that bootstrap sample.
Usage
linear.approx(boot.out, L = NULL, index = 1, type = NULL,
t0 = NULL, t = NULL, ...)
Arguments
boot.out 
An object of class 
L 
A vector containing the empirical influence values for the statistic of
interest. If it is not supplied then 
index 
The index of the variable of interest within the output of

type 
This gives the type of empirical influence values to be calculated. It is
not used if 
t0 
The observed value of the statistic of interest. The input value is used only
if one of 
t 
A vector of bootstrap replicates of the statistic of interest. If 
... 
Any extra arguments required by 
Details
The linear approximation to a bootstrap replicate with frequency vector f
is given by t0 + sum(L * f)/n
in the one sample with an easy extension
to the stratified case. The frequencies are found by calling boot.array
.
Value
A vector of length boot.out$R
with the linear approximations to the
statistic of interest for each of the bootstrap samples.
References
Davison, A.C. and Hinkley, D.V. (1997) Bootstrap Methods and Their Application. Cambridge University Press.
See Also
Examples
# Using the city data let us look at the linear approximation to the
# ratio statistic and its logarithm. We compare these with the
# corresponding plots for the bigcity data
ratio < function(d, w) sum(d$x * w)/sum(d$u * w)
city.boot < boot(city, ratio, R = 499, stype = "w")
bigcity.boot < boot(bigcity, ratio, R = 499, stype = "w")
op < par(pty = "s", mfrow = c(2, 2))
# The first plot is for the city data ratio statistic.
city.lin1 < linear.approx(city.boot)
lim < range(c(city.boot$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(op)