The formal relationship between analytic and bootstrap approaches to parametric inference
File(s)relationship_28march17.pdf (427.23 KB)
Accepted version
Author(s)
Young, GA
Kuffner, TA
DiCiccio, TJ
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.
Date Issued
2017-06-01
Date Acceptance
2017-05-15
Citation
Journal of Statistical Planning and Inference, 2017, 191, pp.81-87
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 http://creativecommons.org/licenses/by-nc-nd/4.0/
Subjects
0104 Statistics
Statistics & Probability
Publication Status
Published