FREQUENCY PROPERTIES OF INFERENCES BASED ON AN INTEGRATED LIKELIHOOD FUNCTION

One approach to likelihood inference for a parameter of interest in the presence of a nuisance parameter is to use an integrated likelihood in which the nuisance parameter is eliminated from the likelihood by integrating with respect to a prior density. In this paper, the frequency properties of point estimators and interval estimators based on an integrated likelihood function are considered. These results are used to study the problem of choosing the prior density so that the resulting integrated likelihood function is useful for non-Bayesian likelihood inference.

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