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February 2020 The numerical bootstrap
Han Hong, Jessie Li
Ann. Statist. 48(1): 397-412 (February 2020). DOI: 10.1214/19-AOS1812

Abstract

This paper proposes a numerical bootstrap method that is consistent in many cases where the standard bootstrap is known to fail and where the $m$-out-of-$n$ bootstrap and subsampling have been the most commonly used inference approaches. We provide asymptotic analysis under both fixed and drifting parameter sequences, and we compare the approximation error of the numerical bootstrap with that of the $m$-out-of-$n$ bootstrap and subsampling. Finally, we discuss applications of the numerical bootstrap, such as constrained and unconstrained M-estimators converging at both regular and nonstandard rates, Laplace-type estimators, and test statistics for partially identified models.

Citation

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Han Hong. Jessie Li. "The numerical bootstrap." Ann. Statist. 48 (1) 397 - 412, February 2020. https://doi.org/10.1214/19-AOS1812

Information

Received: 1 June 2017; Revised: 1 November 2018; Published: February 2020
First available in Project Euclid: 17 February 2020

zbMATH: 07196544
MathSciNet: MR4065167
Digital Object Identifier: 10.1214/19-AOS1812

Subjects:
Primary: 62F40

Rights: Copyright © 2020 Institute of Mathematical Statistics

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Vol.48 • No. 1 • February 2020
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