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Nonparametric BCa bootstrap confidence intervals

Source: R/bca_nonpar.R
bca_nonpar.Rd

Computes nonparametric bias-corrected and accelerated (BCa) bootstrap confidence intervals. Consolidates the functionality of the deprecated bcajack, bcajack2, and bcanon functions.

Usage

bca_nonpar(
  x,
  B,
  func,
  ...,
  accel = c("regression", "jackknife"),
  conf.level = c(0.95, 0.9, 0.8, 0.68),
  n_groups = nrow(x),
  group_reps = 5,
  kl_fraction = 0.333,
  n_jack = 2,
  jack_groups = 12,
  boot_data = NULL,
  verbose = TRUE
)

Arguments

x

An \(n \times p\) data matrix. Rows are observed \(p\)-vectors, assumed independently sampled. If \(p = 1\) then x can be a vector.

B

Number of bootstrap replications (integer).

func

Function computing the parameter of interest. func(x, ...) should return a scalar for any data matrix.

...

Additional arguments passed to func.

accel

Method for estimating acceleration: "regression" (default) uses local regression on bootstrap count vectors nearest to uniform; "jackknife" uses classical delete-one (or delete-group) jackknife influence values.

conf.level

Confidence levels for the intervals (e.g., c(0.95, 0.90, 0.80, 0.68)). Only values in (0, 1) are used.

n_groups

Number of groups for jackknife. Default nrow(x) gives delete-one jackknife. Set smaller (e.g., 20-40) to speed up computation on large datasets.

group_reps

When n_groups < nrow(x), number of random grouping repetitions to average over. Only used with accel = "jackknife".

kl_fraction

Fraction of bootstrap count vectors nearest to uniform used in the local regression. Only used with accel = "regression". Default 1/3.

n_jack

Number of delete-d jackknife repetitions for estimating internal (Monte Carlo) standard error. Set to 0 to skip.

jack_groups

Number of groups per jackknife fold.

boot_data

Optional pre-computed bootstrap data: a list with components Y (B x n count matrix), tt (bootstrap replicates), t0 (original estimate). When provided, B is ignored and no resampling is performed.

verbose

Logical; show progress bar during bootstrap.

Value

An object of class "bcaboot" with components:

limits

9-row matrix of confidence limits (columns: bca, jacksd, std, pct)

stats

2-row matrix of estimates and jackknife SEs (columns: theta, sdboot, z0, a, sdjack)

B_mean

Bootstrap sample size and mean of replicates

ustats

Bias-corrected estimator and its SE

diagnostic

gbca diagnostic (when accel = "regression")

References

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

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")
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)
result <- bca_nonpar(x = Xy, B = 1000, func = rfun, n_groups = 34,
                     verbose = FALSE)
print(result)
#> 
#> ── BCa Bootstrap Confidence Intervals 
#> Method: nonpar (regression acceleration)
#> B = 1000, theta = 0.5065603, sdboot = 0.02988642
#> 
#> Confidence limits:
#>  conf.level    bca.lo    bca.hi    std.lo    std.hi
#>        0.95 0.4205204 0.5544006 0.4479840 0.5651366
#>        0.90 0.4473162 0.5458156 0.4574015 0.5557191
#>        0.80 0.4574096 0.5349201 0.4682593 0.5448613
#>        0.68 0.4654674 0.5272497 0.4768395 0.5362811
#> 
#> Diagnostics:
#> z0 = -0.3318533, a = -0.01267648, sdjack = 0.03047356