Bootstrap bias estimate and correction

bias = mean(replicates) - estimate, corrected value 2 estimate - mean(replicates) – on the OPPOSITE side of the estimate from the replicate mean; using the replicate mean itself doubles the bias instead of removing it, and the direction is tested on the MLE variance, whose bias is exactly -s^2/n. Efron-Tibshirani's Ch. 10 warning travels in the output: the correction adds variance and can raise the MSE.

Usage

morie_bt_bias(theta_hat, theta_b)

Arguments

theta_hat

the statistic on the original data.

theta_b

bootstrap replicates.

Value

list: bias, corrected, estimate, mean_replicate, relative_bias, B, correction_warning, method.

References

Efron (1979); Efron and Tibshirani (1993), Ch. 10.

Examples

morie_bt_bias(1, c(1.1, 1.2, 0.9))$corrected
#> [1] 0.9333333