The formal relationship between analytic and bootstrap approaches to parametric inference

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Title: The formal relationship between analytic and bootstrap approaches to parametric inference
Author(s): Young, GA
Kuffner, TA
DiCiccio, TJ
Item Type: Journal Article
Abstract: Two routes most commonly proposed for accurate inference on a scalar interest parameter in the presence of a (possibly high-dimensional) nuisance parameter are parametric simulation (‘bootstrap’) methods, and analytic procedures based on normal approximation to adjusted forms of the signed root likelihood ratio statistic. Under some null hypothesis of interest, both methods yield p-values which are uniformly distributed to error of third-order in the available sample size. But, given a specific dataset, what is the formal relationship between p-values calculated by the two approaches? We show that the two methodologies give the same inference to second order in general: the analytic p-value calculated from a dataset will agree with the bootstrap p-value constructed from that same dataset to O(n−1), where n is the sample size. In practice, the agreement is often startling.
Publication Date: 1-Jun-2017
Date of Acceptance: 15-May-2017
ISSN: 0378-3758
Publisher: Elsevier
Start Page: 81
End Page: 87
Journal / Book Title: Journal of Statistical Planning and Inference
Volume: 191
Copyright Statement: © 2017, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
Keywords: 0104 Statistics
Statistics & Probability
Publication Status: Published
Appears in Collections:Mathematics
Faculty of Natural Sciences

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