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Grouped Likelihood for the Shifted Power Transformation

1991; Oxford University Press; Volume: 53; Issue: 2 Linguagem: Inglês

10.1111/j.2517-6161.1991.tb01839.x

1467-9868

Anthony C. Atkinson, Luis R. Pericchi, Richard L. Smith,

Statistical Methods and Inference

SUMMARY Estimation of parameters is considered in the shifted power transformation family of models. The ordinary likelihood function is shown to behave poorly, often having no local maximum. It is argued that a grouped likelihood approach avoids these difficulties, and the practical implementation of this approach is considered. Bayesian inference is also considered, though more briefly, and it is argued that there are again difficulties with an ungrouped likelihood approach. The results provide further evidence of the utility of grouped likelihood approaches to inference in non-regular problems.