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 `"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.

### 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.

`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")
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))
```

[Package boot version 1.2-24 Index]