Likelihood Inference for Models with Unobservables: Another View

Details Likelihood Inference for Models with Unobservables: Another View Likelihood Inference for Models with Unobservables: Another View

2010-10-02

arxiv.org/abs/1010.0303v2

Statistical Science 2009, Vol. 24, No. 3, 255-269

Statistics

Methodology

This paper discussed in: [arXiv:1010.0804], [arXiv:1010.0807], [arXiv:1010.0810]. Rejoinder at [arXiv:1010.0814]. Published in

Scientific paper

10.1214/09-STS277

There have been controversies among statisticians on (i) what to model and (ii) how to make inferences from models with unobservables. One such controversy concerns the difference between estimation methods for the marginal means not necessarily having a probabilistic basis and statistical models having unobservables with a probabilistic basis. Another concerns likelihood-based inference for statistical models with unobservables. This needs an extended-likelihood framework, and we show how one such extension, hierarchical likelihood, allows this to be done. Modeling of unobservables leads to rich classes of new probabilistic models from which likelihood-type inferences can be made naturally with hierarchical likelihood.

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