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Statistica Sinica 21 (2011), 433-447





FREQUENCY PROPERTIES OF INFERENCES BASED

ON AN INTEGRATED LIKELIHOOD FUNCTION


Thomas A. Severini


Northwestern University


Abstract: 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.



Key words and phrases: Confidence intervals, local power, nuisance parameters, point estimation.

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