In likelihood ratio tests involving inequality-constrained hypotheses,
the Neyman-Pearson test based on the least favourable parameter value in
a compound null hypothesis can be extremely conservative. The ordinary
parametric bootstrap is generally inconsistent and usually too liberal.
Two methods of correcting the inconsistency of the parametric bootstrap
are proposed: shrinking the constraint set toward the maximum likelihood
estimate and superefficient estimation of the active set of constraints.
Optimal shrinkage adjustment can be determined using bootstrap calibration.
These methods are compared with the double bootstrap, the subsampling
bootstrap, Bayes factors, and Bayesian P-values.
The Bayesian methods are also too liberal if diffuse priors are used.
Geyer, Charles J..
Likelihood Ratio Tests and Inequality Constraints.
School of Statistics, University of Minnesota.
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