Miscellanea. The directed modified profile likelihood in models with many nuisance parameters

Authors: Sartori N.^{1, 2}; Bellio R.^{1, 3}; Salvan A.^{1, 4}; Pace L.⁵

Source: Biometrika, Volume 86, Number 3, September 1999 , pp. 735-742(8)

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Abstract:

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.

Keywords: Exponential family; Higher-order asymptotics; Modi

Language: English

Document Type: Original article

Affiliations: E-mail: pace@dss.uniud.it : 1: Department of Statistics, University of Padova, via S. Francesco 33, I-35121 Padova, Italy 2: E-mail: sartori@hal.stat.unipd.it 3: E-mail: bellio@hal.stat.unipd/it 4: E-mail: salvan@hal.stat.unipd.it 5: Department of Statistics, University of Udine, via Treppo 18, I-33100 Udine, Italy