Interpreting statistical evidence by using imperfect models: robust adjusted likelihood functions
AbstractThe strength of statistical evidence is measured by the likelihood ratio. Two key performance properties of this measure are the probability of observing strong misleading evidence and the probability of observing weak evidence. For the likelihood function associated with a parametric statistical model, these probabilities have a simple large sample structure when the model is correct. Here we examine how that structure changes when the model fails. This leads to criteria for determining whether a given likelihood function is robust (continuing to perform satisfactorily when the model fails), and to a simple technique for adjusting both likelihoods and profile likelihoods to make them robust. We prove that the expected information in the robust adjusted likelihood cannot exceed the expected information in the likelihood function from a true model. We note that the robust adjusted likelihood is asymptotically fully efficient when the working model is correct, and we show that in some important examples this efficiency is retained even when the working model fails. In such cases the Bayes posterior probability distribution based on the adjusted likelihood is robust, remaining correct asymptotically even when the model for the observable random variable does not include the true distribution. Finally we note a link to standard frequentist methodology-in large samples the adjusted likelihood functions provide robust likelihood-based confidence intervals. Copyright 2003 Royal Statistical Society.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Royal Statistical Society in its journal Journal of the Royal Statistical Society: Series B (Statistical Methodology).
Volume (Year): 65 (2003)
Issue (Month): 2 ()
Contact details of provider:
Postal: 12 Errol Street, London EC1Y 8LX, United Kingdom
Web page: http://wileyonlinelibrary.com/journal/rssb
More information through EDIRC
You can help add them by filling out this form.
CitEc Project, subscribe to its RSS feed for this item.
- Tsung-Shan Tsou, 2011. "Likelihood inferences for the link function without knowing the true underlying distributions," Computational Statistics, Springer, vol. 26(3), pages 507-519, September.
- Lemonte, Artur J., 2013. "On the gradient statistic under model misspecification," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 390-398.
- Caterina Conigliani & Andrea Tancredi, 2006. "Comparing parametric and semi-parametric approaches for bayesian cost-effectiveness analyses in health economics," Departmental Working Papers of Economics - University 'Roma Tre' 0064, Department of Economics - University Roma Tre.
- Caterina Conigliani & Andrea Tancredi, 2009. "A Bayesian model averaging approach for cost-effectiveness analyses," Health Economics, John Wiley & Sons, Ltd., vol. 18(7), pages 807-821.
- Shen, Chung-Wei & Tsou, Tsung-Shan & Balakrishnan, N., 2011. "Robust likelihood inference for regression parameters in partially linear models," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1696-1714, April.
- Hoch, Jeffrey S. & Blume, Jeffrey D., 2008. "Measuring and illustrating statistical evidence in a cost-effectiveness analysis," Journal of Health Economics, Elsevier, vol. 27(2), pages 476-495, March.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Wiley-Blackwell Digital Licensing) or (Christopher F. Baum).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.