# Bias Correction with Jackknife, Bootstrap, and Taylor Series

arXiv: https://arxiv.org/abs/1709.06183 · HTML: https://mlsanity.com/paper/1709.06183/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Sep 2017.

## Built on by (most cited first, 4 of 4)

- [Debiasing Conditional Stochastic Optimization](https://mlsanity.com/paper/2304.10613/) (2023)
- [Improving Fairness and Mitigating MADness in Generative Models](https://mlsanity.com/paper/2405.13977/) (2024)
- [Robust Policy Optimization to Prevent Catastrophic Forgetting](https://mlsanity.com/paper/2602.08813/) (2026)
- [Orthogonal Bootstrap: Efficient Simulation of Input Uncertainty](https://mlsanity.com/paper/2404.19145/) (2024)

## Abstract (arXiv)

We analyze bias correction methods using jackknife, bootstrap, and Taylor series. We focus on the binomial model, and consider the problem of bias correction for estimating f(p), where f ∈ C[0,1] is arbitrary. We characterize the supremum norm of the bias of general jackknife and bootstrap estimators for any continuous functions, and demonstrate the in delete-d jackknife, different values of d may lead to drastically different behaviors in jackknife. We show that in the binomial model, iterating the bootstrap bias correction infinitely many times may lead to divergence of bias and variance, and demonstrate that the bias properties of the bootstrap bias corrected estimator after r-1 rounds are of the same order as that of the r-jackknife estimator if a bounded coefficients condition is satisfied.