bcajack2 {bcaboot} | R Documentation |
Nonparametric bias-corrected 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 time-consuming, 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 i-th 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 i-th 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 non-negative 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 bias-corrected 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)