Bias Correction with Jackknife, Bootstrap, and Taylor Series

Jiantao Jiao, Yanjun Han

Research output: Contribution to journalArticlepeer-review


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\in 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.

Original languageEnglish (US)
Article number8970278
Pages (from-to)4392-4418
Number of pages27
JournalIEEE Transactions on Information Theory
Issue number7
StatePublished - Jul 2020


  • Bootstrap
  • approximation theory
  • bias correction
  • functional estimation
  • jackknife

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


Dive into the research topics of 'Bias Correction with Jackknife, Bootstrap, and Taylor Series'. Together they form a unique fingerprint.

Cite this