linear.approx {boot}  R Documentation 
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.
linear.approx(boot.out, L=NULL, index=1, type=NULL, t0=NULL, t=NULL, ...)
boot.out 
An object of class "boot" representing a nonparametric bootstrap. It will
usually be created by the function boot .

L 
A vector containing the empirical influence values for the statistic of
interest. If it is not supplied then L is calculated through a call
to empinf .

index 
The index of the variable of interest within the output of
boot.out$statistic .

type 
This gives the type of empirical influence values to be calculated. It is
not used if L is supplied. The possible types of empirical influence
values are described in the helpfile for empinf .

t0 
The observed value of the statistic of interest. The input value is used only
if one of t or L is also supplied. The default value is
boot.out$t0[index] . If t0 is supplied but neither t nor L are supplied
then t0 is set to boot.out$t0[index] and a warning is generated.

t 
A vector of bootstrap replicates of the statistic of interest. If t0 is
missing then t is not used, otherwise it is used to calculate the empirical
influence values (if they are not supplied in L ).

... 
Any extra arguments required by boot.out$statistic . These are needed if
L is not supplied as they are used by empinf to calculate empirical
influence values.

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
.
A vector of length boot.out$R
with the linear approximations to the
statistic of interest for each of the bootstrap samples.
Davison, A.C. and Hinkley, D.V. (1997) Bootstrap Methods and Their Application. Cambridge University Press.
# Using the city data let us look at the linear approximation to the # ratio statistic and its logarithm. We compare these with the # corresponding plots for the bigcity data ratio < function(d, w) sum(d$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))