linear.approx {boot}

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 "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 help 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.

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

boot, empinf, control

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)