Lindley's problem, relating to the conditions under which there is formal mathematical equivalence between Bayesian solutions and confidence theory solutions, is discussed. A result concerning location parameters is extended. The corresponding asymptotic theory is developed and a modification of the problem is also discussed.
Summary
The problem of formal equivalence between confidence points and Bayesian probability points in situations where there are several unknown parameters is discussed, and the relevant asymptotic formulae are derived to O(n–½).
SUMMARY
Series expansions for confidence limits based on consistent estimators are obtained in the presence of nuisance parameters. The maximum likelihood estimator is treated as a special case and the necessary characteristics of its sampling distribution are obtained in terms of basic quantities derivable from the likelihood function. The theory is applied to the problem of setting separate confidence limits for the scale and shape parameters of the Weibull distribution. Comparisons are made with earlier simulation studies.
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