Accurate Procedures for Approximate Bayesian and Conditional Inference Withoutthe Need for Orthogonal Parameters

摘要

This paper concerns methods to construct approximate confidence limits for ascalar parameter in the presence of nuisance parameters. The methods are based on Bayesian procedures discussed by Peers (1965) and Stein (1985), in which prior density is chosen so that the posterior quantiles of iP are approximate confidence limits with coverage error of order O(n-1) ) under repeated sampling. Multidimensional integration of the posterior density is avoided by using approximations of marginal densities and distribution functions; thus, adjustments are obtained that 4 Drove the standard normal approximation to the distributions of signed roots of the profile and conditional likelihood ratio statistics for psi. The necessary prior densities are easy to specify when the nuisance parameters are orthogonal to the parameter of interest, and this simplicities exploited in developing the methods. However, the need for explicit specification of an orthogonal parameterization is alleviated by approximating the Jacobian of a transformation to orthogonality. The methods are illustrated and compared with other procedures in some examples involving exponential families.