2017/09/18 by Jiantao Jiao, Yanjun Han, Jiao, Jiantao +1
Mathematics · #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Machine Learning (cs.LG) #Statistical Distribution Estimation and Applications #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1709.06183
openalex publication_date 2017/09/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.