Debiased inference, wild bootstrap, and Efron’s bootstrap

This vignette covers inference for the debiased Cox-Lasso estimator. The debiased estimator targets full-model coefficients; it is conceptually distinct from inference for an unpenalized refit on a selected support.

Debiased estimator

Let fit be the result of coxlasso_fit(). The package applies the score-based correction and estimates the inverse-information directions by nodewise regression.

db <- coxlasso_debias(fit)
summary(db)

The implementation keeps the original Cox-Lasso pilot and the estimated nodewise correction available for subsequent bootstrap inference.

Wild bootstrap and Efron’s bootstrap

Both bootstrap constructions operate on the debiased representation rather than repeating Cox-Lasso fitting and nodewise estimation in every bootstrap sample.

db_boot <- coxlasso_boot(
  fit,
  inference = "debiased",
  type = c("wild", "efron"),
  B = 500,
  conf_level = 0.95,
  seed = 2026
)
summary(db_boot)

The string "efron" is the software argument naming Efron’s bootstrap. In prose, the method is referred to as Efron’s bootstrap.

Interpretation

The wild bootstrap and Efron’s bootstrap approximate uncertainty for the debiased full-model coefficient target. They should not be interpreted as fixed-support or selection-conditional inference. The methodological details and theoretical justification are developed in Wild Bootstrap and Efron’s Bootstrap for Debiased Cox Regression.