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Parametric BCa bootstrap confidence intervals

Source: R/bca_par.R
bca_par.Rd

Computes parametric bootstrap confidence intervals for a real-valued parameter theta in a p-parameter exponential family.

Usage

bca_par(
  t0,
  tt,
  bb,
  conf.level = c(0.95, 0.9, 0.8, 0.68),
  n_jack = 6,
  jack_groups = 10,
  truncation = 0.001,
  kl_fraction = 0.333,
  conf_density = FALSE,
  func
)

Arguments

t0

Observed estimate of theta, usually by maximum likelihood.

tt

A vector of B parametric bootstrap replications of theta.

bb

A B by p matrix of natural sufficient vectors, where p is the dimension of the exponential family.

conf.level

Confidence levels for the intervals.

n_jack

Number of jackknife repetitions for internal SE. Set to 0 to skip.

jack_groups

Number of groups per jackknife fold.

truncation

Truncation parameter for acceleration calculation. Can be a vector to compute acceleration at multiple levels.

kl_fraction

Proportion of "nearby" b vectors used in gradient estimation.

conf_density

Logical; if TRUE, return BCa confidence density weights.

func

Optional function for ABC (analytical bootstrap) limits.

Value

An object of class "bcaboot" with components:

limits

9-row matrix of confidence limits

stats

2-row matrix of estimates and jackknife SEs

B_mean

Bootstrap sample size and mean of replicates

ustats

Bias-corrected estimator and its SE

abc

ABC limits and stats (when func provided)

conf_density

Confidence density weights (when requested)

accel_matrix

Acceleration at multiple truncation levels

References

Efron B (1987). Better bootstrap confidence intervals. JASA 82, 171-200.

DiCiccio T and Efron B (1992). More accurate confidence intervals in exponential families. Biometrika, 231-245.

Efron B and Narasimhan B (2020). The Automatic Construction of Bootstrap Confidence Intervals. Journal of Computational and Graphical Statistics, 29(3), 608-619. doi:10.1080/10618600.2020.1714633

Examples

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)$adj.r.squared
y.star <- sapply(mu.hat, rnorm, n = 500, sd = sigma.hat)
tt <- apply(y.star, 1, function(y) summary(lm(y ~ X - 1))$adj.r.squared)
b.star <- y.star %*% X
set.seed(1234)
bca_par(t0 = t0, tt = tt, bb = b.star)
#> 
#> ── BCa Bootstrap Confidence Intervals 
#> Method: par
#> B = 500, theta = 0.5065862, sdboot = 0.0297771
#> 
#> Confidence limits:
#>  conf.level    bca.lo    bca.hi    std.lo    std.hi
#>        0.95 0.4472066 0.5565305 0.4482242 0.5649483
#>        0.90 0.4518055 0.5478429 0.4576072 0.5555652
#>        0.80 0.4626100 0.5349231 0.4684253 0.5447471
#>        0.68 0.4706893 0.5267426 0.4769741 0.5361983
#> 
#> Diagnostics:
#> z0 = -0.3107377, a = 0.01129753