bcapar {bcaboot} | R Documentation |
bcapar computes parametric bootstrap confidence intervals for a real-valued parameter theta in a p-parameter exponential family. It is described in Section 4 of the reference below.
bcapar(
t0,
tt,
bb,
alpha = c(0.025, 0.05, 0.1, 0.16),
J = 10,
K = 6,
trun = 0.001,
pct = 0.333,
cd = 0,
func
)
t0 |
Observed estimate of theta, usually by maximum likelihood. |
tt |
A vector of parametric bootstrap replications of theta of
length |
bb |
A |
alpha |
percentiles desired for the bca confidence limits. One
only needs to provide |
J , K |
Parameters controlling the jackknife estimates of Monte
Carlo error: |
trun |
Truncation parameter used in the calculation of the
acceleration |
pct |
Proportion of "nearby" b vectors used in the calculation
of |
cd |
If cd is 1 the bca confidence density is also returned; see Section 11.6 in reference Efron and Hastie (2016) below |
func |
Function |
a named list of several items:
lims : Bca confidence limits (first column) and the standard
limits (fourth column). Also the abc limits (fifth column) if
func
is provided. The second column, jacksd
, are the
jackknife estimates of Monte Carlo error; pct
, the third
column are the proportion of the replicates tt
less than each
bcalim
value
stats : Estimates and their jackknife Monte Carlo errors:
theta
= \hat{\theta}
; sd
, the bootstrap standard deviation
for \hat{\theta}
; a
the acceleration estimate; az
another
acceleration estimate that depends less on extreme values of tt
;
z0
the bias-correction estimate; A
the big-A measure of raw
acceleration; sdd
delta method estimate for standard deviation of
\hat{\theta}
; mean
the average of tt
abcstats : The abc estimates of a
and z0
, returned if func
was provided
ustats : The bias-corrected estimator 2 * t0 - mean(tt)
. ustats
gives ustat
, an estimate sdu
of its sampling error, and jackknife
estimates of monte carlo error for both ustat
and sdu
. Also given
is B
, the number of bootstrap replications
seed : The random number state for reproducibility
DiCiccio T and Efron B (1996). Bootstrap confidence intervals. Statistical Science 11, 189-228
T. DiCiccio and B. Efron. More accurate confidence intervals in exponential families. Biometrika (1992) p231-245.
Efron B (1987). Better bootstrap confidence intervals. JASA 82, 171-200
B. Efron and T. Hastie. Computer Age Statistical Inference. Cambridge University Press, 2016.
B. Efron and B. Narasimhan. Automatic Construction of Bootstrap Confidence Intervals, 2018.
data(diabetes, package = "bcaboot")
X <- diabetes$x
y <- scale(diabetes$y, center = TRUE, scale = FALSE)
lm.model <- lm(y ~ X - 1)
mu.hat <- lm.model$fitted.values
sigma.hat <- stats::sd(lm.model$residuals)
t0 <- summary(lm.model)$adj.r.squared
y.star <- sapply(mu.hat, rnorm, n = 1000, sd = sigma.hat)
tt <- apply(y.star, 1, function(y) summary(lm(y ~ X - 1))$adj.r.squared)
b.star <- y.star %*% X
set.seed(1234)
bcapar(t0 = t0, tt = tt, bb = b.star)