control {boot}  R Documentation 
Control Variate Calculations
Description
This function will find control variate estimates from a bootstrap output object. It can either find the adjusted bias estimate using postsimulation balancing or it can estimate the bias, variance, third cumulant and quantiles, using the linear approximation as a control variate.
Usage
control(boot.out, L = NULL, distn = NULL, index = 1, t0 = NULL,
t = NULL, bias.adj = FALSE, alpha = NULL, ...)
Arguments
boot.out 
A bootstrap output object returned from 
L 
The empirical influence values for the statistic of interest. If

distn 
If present this must be the output from 
index 
The index of the variable of interest in the output of

t0 
The observed value of the statistic of interest on the original data
set 
t 
The bootstrap replicate values of the statistic of interest. This
argument is used only if 
bias.adj 
A logical variable which if 
alpha 
The alpha levels for the required quantiles if 
... 
Any additional arguments that 
Details
If bias.adj
is FALSE
then the linear approximation to
the statistic is found and evaluated at each bootstrap replicate.
Then using the equation T* = Tl*+(T*Tl*), moment estimates can
be found. For quantile estimation the distribution of the linear
approximation to t
is approximated very accurately by
saddlepoint methods, this is then combined with the bootstrap
replicates to approximate the bootstrap distribution of t
and
hence to estimate the bootstrap quantiles of t
.
Value
If bias.adj
is TRUE
then the returned value is the
adjusted bias estimate.
If bias.adj
is FALSE
then the returned value is a list
with the following components
L 
The empirical influence values used. These are the input values if
supplied, and otherwise they are the values calculated by

tL 
The linear approximations to the bootstrap replicates 
bias 
The control estimate of bias using the linear approximation to

var 
The control estimate of variance using the linear approximation to

k3 
The control estimate of the third cumulant using the linear
approximation to 
quantiles 
A matrix with two columns; the first column are the alpha levels
used for the quantiles and the second column gives the corresponding
control estimates of the quantiles using the linear approximation to

distn 
An output object from 
References
Davison, A.C. and Hinkley, D.V. (1997) Bootstrap Methods and Their Application. Cambridge University Press.
Davison, A.C., Hinkley, D.V. and Schechtman, E. (1986) Efficient bootstrap simulation. Biometrika, 73, 555–566.
Efron, B. (1990) More efficient bootstrap computations. Journal of the American Statistical Association, 55, 79–89.
See Also
boot
, empinf
, k3.linear
, linear.approx
, saddle.distn
, smooth.spline
, var.linear
Examples
# Use of control variates for the variance of the airconditioning data
mean.fun < function(d, i)
{ m < mean(d$hours[i])
n < nrow(d)
v < (n1)*var(d$hours[i])/n^2
c(m, v)
}
air.boot < boot(aircondit, mean.fun, R = 999)
control(air.boot, index = 2, bias.adj = TRUE)
air.cont < control(air.boot, index = 2)
# Now let us try the variance on the log scale.
air.cont1 < control(air.boot, t0 = log(air.boot$t0[2]),
t = log(air.boot$t[, 2]))