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Biometrika 1999 86(3):735-742; doi:10.1093/biomet/86.3.735
© 1999 by Biometrika Trust
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Miscellanea. The directed modified profile likelihood in models with many nuisance parameters

N SartoriA1,A2, R BellioA1,A3, A SalvanA1,A4 and L PaceA5

A1 Department of Statistics, University of Padova, via S. Francesco 33, I-35121 Padova, Italy A2 E-mail: sartori@hal.stat.unipd.it A3 E-mail: bellio@hal.stat.unipd/it A4 E-mail: salvan@hal.stat.unipd.it A5 Department of Statistics, University of Udine, via Treppo 18, I-33100 Udine, Italy E-mail: pace@dss.uniud.it

The modified profile likelihood is a higher-order approximation to a conditional or a marginal likelihood, when either exists. The directed likelihood based on the modified profile likelihood is standard normal only to first order. In practice, however, it usually achieves most of the distributional improvement obtained by higher-order methods. This note elucidates this point with particular attention to models with many nuisance parameters.

Key Words: Exponential family; Higher-order asymptotics; Modified directed likelihood decomposition; Nuisance parameter


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