期刊
IEEE TRANSACTIONS ON INFORMATION THEORY
卷 66, 期 7, 页码 4392-4418出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIT.2020.2969439
关键词
Taylor series; Estimation; Analytical models; Entropy; Approximation methods; Electrical engineering; Mathematical model; Bootstrap; jackknife; bias correction; functional estimation; approximation theory
资金
- National Science Foundation (NSF) [IIS-1901252, CCF-1909499]
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 is an element of 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.
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