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=F, 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
.
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, 555-566.
Efron, B. (1990) More efficient bootstrap computations. Journal of the American Statistical Association, 55, 79-89.
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$hours[i])/n^2 c(m, v) } data(aircondit) air.boot <- boot(aircondit, mean.fun, R=999) control(air.boot,index=2,bias.adj=T) air.cont <- control(air.boot, index=2) # Now let us try the variance on the log scale. air.cont1 <- control(air.boot, t0=log(air.boot$t0[2]), t=log(air.boot$t[,2]))