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Importance of interpolation when constructing double‐bootstrap confidence intervals
Author(s) -
Hall Peter,
Lee Stephen M.S.,
Young G. Alastair
Publication year - 2000
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/1467-9868.00245
Subject(s) - confidence interval , interpolation (computer graphics) , monte carlo method , mathematics , statistics , bootstrap model , context (archaeology) , standard error , sampling (signal processing) , linear interpolation , algorithm , computer science , mathematical analysis , physics , particle decay , animation , boson , paleontology , computer graphics (images) , filter (signal processing) , particle physics , polynomial , computer vision , biology
We show that, in the context of double‐bootstrap confidence intervals, linear interpolation at the second level of the double bootstrap can reduce the simulation error component of coverage error by an order of magnitude. Intervals that are indistinguishable in terms of coverage error with theoretical, infinite simulation, double‐bootstrap confidence intervals may be obtained at substantially less computational expense than by using the standard Monte Carlo approximation method. The intervals retain the simplicity of uniform bootstrap sampling and require no special analysis or computational techniques. Interpolation at the first level of the double bootstrap is shown to have a relatively minor effect on the simulation error.