We consider inference on a vector-valued parameter of interest in a linear exponential family, in the presence of a finite-dimensional nuisance parameter. Based on higher-order asymptotic theory for likelihood, we propose a directional test whose <italic>p</italic>-value is computed using one-dimensional...

A tolerance region is a map from the sample space of one statistical model to the event space of a second statistical model having the same parameter. This paper derives an optimum [beta]-expectation tolerance region for the multivariate regression model. A measure of power is proposed and...

For a statistical model with data, likelihood for the scalar or vector full parameter &thgr;, of dimension p say, is typically well defined and easily computed. In this paper, we investigate likelihood for a component parameter &psgr;(&thgr;) of dimension d p and make use of the recent likelihood theory that...

Higher-order approximations to p-values can be obtained from the loglikelihood function and a reparameterization that can be viewed as a canonical parameter in an exponential family approximation to the model. This approach clarifies the connection between Skovgaard (1996) and Fraser et al....

Discrete data, particularly count and contingency table data, are typically analysed by using methods that are accurate to first order, such as normal approximations for maximum likelihood estimators. By contrast continuous data can quite generally be analysed by using third-order procedures,...

Barndorff-Nielsen's formula (normed likelihood with constant-information metric) has been proffered as an approximate conditional distribution for the maximum-likelihood estimate, based on likelihood functions. Asymptotic justifications are available and the formula coincides with the...

We investigate the choice of default priors for use with likelihood for Bayesian and frequentist inference. Such a prior is a density or relative density that weights an observed likelihood function, leading to the elimination of parameters that are not of interest and then a density-type...