We introduce a new method to robustifying inference that can be applied in any situation where a parametric likelihood is available. The key feature is that data from the postulated parametric models are assumed to be measured with error where the measurement error distribution is chosen to produce the occasional gross errors found in data. We show that the tails of the error-contamination model control the properties (boundedness, redescendingness) of the resulting influence functions, with heavier tails in the error contamination model producing more robust estimators. In the application to location-scale models with independent and identically distributed data, the resulting analytically-intractable likelihoods are approximated via Monte Carlo integration. In the application to time series models, we propose a Bayesian approach to the robust estimation of time series parameters. We use Markov Chain Monte Carlo (MCMC) to estimate the parameters of interest and also the gross errors. The latter are used as outlier diagnostics.
| Identifer | oai:union.ndltd.org:NCSU/oai:NCSU:etd-08112005-222926 |
| Date | 16 August 2005 |
| Creators | Wang, Qiong |
| Contributors | David D. Dickey, Dennis D. Boos, Leonard A. Stefanski, Marc G. Genton |
| Publisher | NCSU |
| Source Sets | North Carolina State University |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://www.lib.ncsu.edu/theses/available/etd-08112005-222926/ |
| Rights | unrestricted, I hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to NC State University or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report. |
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