bcajack2 {bcaboot}  R Documentation 
Nonparametric biascorrected and accelerated bootstrap confidence limits
Description
This function is a version of bcajack
that allows
all the recomputations of the original statistic function
f
to be carried out separately. This is an advantage
if f
is timeconsuming, in which case the B
replications for the nonparametric bca calculations might need
to be done on a distributed basis.
To use bcajack2
in this mode, we first compute a list Blist
via
Blist < list(Y = Y, tt = tt, t0 = t0)
. Here tt
is a vector of
length B
having ith entry tt[i] < func(x[Ii,], ...)
, where x
is the n \times p
data matrix and Ii
is a bootstrap vector
of (observation) indices. Y
is a B
by n
count matrix,
whose ith row is the counts corresponding to Ii
. For example if
n = 5 and Ii = (2, 5, 2, 1, 4)
, then Yi = (1, 2, 0, 1, 1)
. Having computed Blist
, bcajack2
is invoked as
bcajack2(Blist)
without need to enter the function func
.
Usage
bcajack2(
x,
B,
func,
...,
m = nrow(x),
mr,
pct = 0.333,
K = 2,
J = 12,
alpha = c(0.025, 0.05, 0.1, 0.16),
verbose = TRUE
)
Arguments
x 
an 
B 
number of bootstrap replications. 
func 
function 
... 
additional arguments for 
m 
an integer less than or equal to 
mr 
if 
pct 

K 
a nonnegative integer. If 
J 
the number of groups into which the bootstrap replications are split 
alpha 
percentiles desired for the bca confidence limits. One
only needs to provide 
verbose 
logical for verbose progress messages 
Value
a named list of several items

lims : first column shows the estimated bca confidence limits at the requested alpha percentiles. These can be compared with the standard limits
\hat{\theta} + \hat{\sigma}z_{\alpha}
, third column. The second columnjacksd
gives the internal standard errors for the bca limits, quite small in the example. Column 4,pct
, gives the percentiles of the ordered B bootstrap replications corresponding to the bca limits, eg the 897th largest replication equalling the .975 bca limit .557. 
stats : top line of stats shows 5 estimates: theta is
func(x)
, original point estimate of the parameter of interest;sdboot
is its bootstrap estimate of standard error;z0
is the bca bias correction value, in this case quite negative;a
is the acceleration, a component of the bca limits (nearly zero here);sdjack
is the jackknife estimate of standard error for theta. Bottom line gives the internal standard errors for the five quantities above. This is substantial forz0
above. 
B.mean : bootstrap sample size B, and the mean of the B bootstrap replications
\hat{\theta^*}

ustats : The biascorrected estimator
2 * t0  mean(tt)
, and an estimatesdu
of its sampling error 
seed : The random number state for reproducibility
Examples
data(diabetes, package = "bcaboot")
Xy < cbind(diabetes$x, diabetes$y)
rfun < function(Xy) {
y < Xy[, 11]
X < Xy[, 1:10]
summary(lm(y~X) )$adj.r.squared
}
set.seed(1234)
bcajack2(x = Xy, B = 1000, func = rfun, m = 40, verbose = FALSE)