 Quantifying the failure of bootstrap likelihood ratio testsMathias Drton and Benjamin Williams Biometrika, 2011, vol. 98, issue 4, 919-934 Abstract: When testing geometrically irregular parametric hypotheses, the bootstrap is an intuitively appealing method to circumvent difficult distribution theory. It has been shown, however, that the usual bootstrap is inconsistent in estimating the asymptotic distributions involved in such problems. This paper is concerned with the asymptotic size of likelihood ratio tests when critical values are computed using the inconsistent bootstrap. We clarify how the asymptotic size of such a test can be obtained from the size of the corresponding bootstrap test in the relevant limiting normal experiment. For boundary problems, that is, hypotheses given by convex cones, we show the bootstrap test to always be anticonservative, and we compute the size numerically for different two-dimensional examples. The examples illustrate that the size can be below or above the nominal level, and reveal that the relationship between the size of the test and the geometry of the considered hypotheses is surprisingly subtle. Copyright 2011, Oxford University Press. Date: 2011 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:oup:biomet:v:98:y:2011:i:4:p:919-934 Ordering information: This journal article can be ordered from Access Statistics for this article Biometrika is currently edited by Paul Fearnhead More articles in Biometrika from Biometrika Trust Oxford University Press, Great Clarendon Street, Oxford OX2 6DP, UK. |
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