2009/08/01 by Youngjo Lee, J. A. Nelder, John A. Nelder
Mathematics · #Advanced Statistical Methods and Models #Artificial intelligence #Computer science #Econometrics #Inference #Likelihood function #Marginal likelihood #Mathematics #Maximum likelihood #Probabilistic logic #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistical inference #Statistical model #Statistics #stat.ME
paper · pdf · doi:10.1214/09-sts277
published as Statistical Science 2009, Vol. 24, No. 3, 255-269 · This paper discussed in: [arXiv:1010.0804], [arXiv:1010.0807], [arXiv:1010.0810]. Rejoinder at [arXiv:1010.0814]. Published in at http://dx.doi.org/10.1214/09-STS277 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org)
openalex publication_date 2009/08/01 · arxiv created 2010/10/06 · arxiv updated 2010/10/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.