Relevance weighted likelihood for dependent data |
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| Authors: | Feifang Hu William F. Rosenberger James V. Zidek |
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| Affiliation: | (1) Department of Statistics and Applied Probability, National University of Singapore, Singapore 119260 (e-mail: stahuff@stat.nus.sg.edu), SG;(2) Department of Mathematics and Statistics, University of Maryland, Baltimore County, 1000 Hilltop Circle, Baltimore, MD 21250, U.S.A. (e-mail: billr@math.umbc.edu), US;(3) Department of Epidemiology and Preventive Medicine, University of Maryland School of Medicine, Baltimore, MD, U.S.A., US;(4) Department of Statistics, University of British Columbia, Vancouver, BC V6T 1Z2, Canada (e-mail: jim@stat.ubc.ca), CA |
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| Abstract: | The relevance-weighted likelihood function weights individual contributions to the likelihood according to their relevance for the inferential problem of interest. Consistency and asymptotic normality of the weighted maximum likelihood estimator were previously proved for independent sequences of random variables. We extend these results to apply to dependent sequences, and, in so doing, provide a unified approach to a number of diverse problems in dependent data. In particular, we provide a heretofore unknown approach for dealing with heterogeneity in adaptive designs, and unify the smoothing approach that appears in many foundational papers for independent data. Applications are given in clinical trials, psychophysics experiments, time series models, transition models, and nonparametric regression. Received: April 2000 |
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| Keywords: | : Adaptive designs asymptotic normality consistency generalized estimating equations martingales nonparametric regression smoothing autoregression model urn model |
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