control {boot} | R Documentation |
This function will find control variate estimates from a bootstrap output object. It can either find the adjusted bias estimate using post-simulation balancing or it can estimate the bias, variance, third cumulant and quantiles, using the linear approximation as a control variate.
control(boot.out, L=NULL, distn=NULL, index=1, t0=NULL, t=NULL, bias.adj=FALSE, alpha=NULL, ...)
boot.out |
A bootstrap output object returned from boot . The bootstrap replicates must
have been generated using the usual nonparametric bootstrap.
|
L |
The empirical influence values for the statistic of interest. If L is not
supplied then empinf is called to calculate them from boot.out .
|
distn |
If present this must be the output from smooth.spline giving the distribution
function of the linear approximation. This is used only if bias.adj is
FALSE . Normally this would be found using a saddlepoint approximation.
If it is not supplied in that case then it is calculated by
saddle.distn .
|
index |
The index of the variable of interest in the output of boot.out$statistic .
|
t0 |
The observed value of the statistic of interest on the original data set
boot.out$data . This argument is used only if bias.adj is FALSE . The
input value is ignored if t is not also supplied. The default value is
is boot.out$t0[index] .
|
t |
The bootstrap replicate values of the statistic of interest. This argument
is used only if bias.adj is FALSE . The input is ignored if t0 is not
supplied also. The default value is boot.out$t[,index] .
|
bias.adj |
A logical variable which if TRUE specifies that the adjusted bias estimate
using post-simulation balance is all that is required. If bias.adj is
FALSE (default)
then the linear approximation to the statistic is calculated and used as a
control variate in estimates of the bias, variance and third cumulant as well as
quantiles.
|
alpha |
The alpha levels for the required quantiles if bias.adj is FALSE .
|
... |
Any additional arguments that boot.out$statistic requires. These are passed
unchanged every time boot.out$statistic is called. boot.out$statistic is
called once if bias.adj is TRUE , otherwise it may be called by empinf for
empirical influence calculations if L is not supplied.
|
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
.
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 empinf .
|
tL |
The linear approximations to the bootstrap replicates t of the statistic of
interest.
|
bias |
The control estimate of bias using the linear approximation to t as a control
variate.
|
var |
The control estimate of variance using the linear approximation to t as a
control variate.
|
k3 |
The control estimate of the third cumulant using the linear approximation to
t as a control variate.
|
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 t as a control
variate.
|
distn |
An output object from smooth.spline describing the saddlepoint approximation
to the bootstrap distribution of the linear approximation to t . If distn
was supplied on input then
this is the same as the input otherwise it is calculated by a call to
saddle.distn .
|
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, 555566.
Efron, B. (1990) More efficient bootstrap computations. Journal of the American Statistical Association, 55, 7989.
boot
, empinf
, k3.linear
, linear.approx
, saddle.distn
, smooth.spline
, var.linear
library(modreg) # for smooth.spline # Use of control variates for the variance of the air-conditioning data mean.fun <- function(d, i) { m <- mean(d$hours[i]) n <- nrow(d) v <- (n-1)*var(d$hours[i])/n^2 c(m, v) } data(aircondit) air.boot <- boot(aircondit, mean.fun, R=999) control(air.boot,index=2,bias.adj=TRUE) air.cont <- control(air.boot, index=2) # Now let us try the variance on the log scale. air.cont1 <- control(air.boot, t0=log(air.boot$t0[2]), t=log(air.boot$t[,2]))