Loh exact bootstrap calibration of the t interval

beta_hat_i = 1 - Phi(|t*_i|) per bootstrap sample (Loh Eq. 2); alpha' is the 2a-quantile of the beta_hat_i and the interval is the normal-theory interval at level alpha'. Sec. 2.2: z_{1-alpha'} equals the (1-2a)-quantile of |t*|, so the result IS the bootstrap-t interval; the identity gap is reported.

Usage

morie_btcalib(x, alpha = 0.05, B = 1000, seed = 0)

Arguments

x: Numeric sample.
alpha: Two-sided non-coverage (0.05 = 95%).
B: Bootstrap samples.
seed: SplitMix64 seed (mirrors the Python arm).

Value

A list with elements estimate, lower, upper, alpha_prime, z_calibrated, identity_gap, alpha, B, seed, method.

References

Loh, W.-Y. (1991). Bootstrap calibration for confidence interval construction and selection. Statistica Sinica, 1(2), 477-491.

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
morie_btcalib(V)
#> $estimate
#> [1] 4.5
#> 
#> $lower
#> [1] 2.388474
#> 
#> $upper
#> [1] 6.611526
#> 
#> $alpha_prime
#> [1] 0.007380703
#> 
#> $z_calibrated
#> [1] 2.43818
#> 
#> $identity_gap
#> [1] 1.776357e-15
#> 
#> $alpha
#> [1] 0.05
#> 
#> $B
#> [1] 1000
#> 
#> $seed
#> [1] 0
#> 
#> $method
#> [1] "Loh (1991) exact bootstrap calibration (Eqs. 1-2)"
#>