concomitants.bootstrap(x, subset.statistic = <all>, L = resampGetL(x), group, treatment, conv.factor = 0.1, frame.eval = <<see below>>)
qDiscreteMean
. A nonzero
value convolves the discrete distribution with a normal distribution;
a small value like 0.1 improves stability, a larger value like
n/(n-1)
adds enough variance that the variance of the result
is
s^2/n
where
s
is calculated with a divisor of
(n-1)
.
x
can be found.
You need to specify this if objects can't be found by their
original names, or have changed; see
.
"concomitants"
which inherits from
"bootstrap"
.
This is the same as
x
, except for components:
L
"call"
,
"estimate"
and
"replicates"
from
x
.
This function adjusts the distribution of the bootstrap replicates, based
on difference between the observed and exact
distributions of a linear approximation.
Given a vector
L
such as that created by
(empirical influence function) or
(influence, jackknife, or regression methods),
this function will
(1) evaluate the linear approximation for bootstrap samples, e.g.
Lstar=indexMeans(L,resampGetIndices(x))
,
(2) compute saddlepoint approximations for
quantiles of the distribution of
Lstar
using
,
then (3) adjust the
replicates
component of the bootstrap object
based on the observed values of the linear approximation for bootstrap
samples and the corresponding quantiles.
This implementation uses
smooth.spline
to allow
the relationship between
Lstar
and the statistic to be curvilinear.
The higher the correlation between
Lstar
and a smooth monotone
transformation of the statistic being bootstrapped the more accurate
the result is.
Do, K. and Hall, P. (1992), "Distribution Estimation using Concomitants of Order Statistics, with Application to Monte Carlo Simulation for the Bootstrap," Journal of the Royal Statistical Society Series B, 54(2), 595-607.
Efron, B. (1990), "More Efficient Bootstrap Computations," Journal of the American Statistical Society, 85, 79-89.
Hesterberg, T.C. (1995), "Tail-Specific Linear Approximations for Efficient Bootstrap Simulations," Journal of Computational and Graphical Statistics, 4, 113-133.
Hesterberg, T.C. (1997), "Fast Bootstrapping by Combining Importance Sampling and Concomitants," Computing Science and Statistics, 29(2), 72-78.
For an annotated list of functions in the package, including other high-level resampling functions, see: .
bfit <- bootstrap(qexp(ppoints(50)), mean) abfit <- concomitants(bfit) bfit # Bias should be zero, but differs due to random variation abfit # Bias is very near zero qqnorm(bfit) qqnorm(abfit) # much less random variation bfit <- bootstrap(1:50, var) abfit <- concomitants(bfit) bfit abfit plot(bfit) plot(abfit)