Abstract:
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We consider three classes of shrinkage-type approaches: (1) Empirical Bayes-type shrinkage, (2) Maximum penalized likelihood, and (3) Hierarchical Bayes to model the association of an outcome at time t (e.g. mortality counts) with an exposure measured at times t, ., t-L (e.g. air particulate matter levels) in classical time series setting. The overarching goal is to reconcile between an unbiased and model-free estimator (e.g. maximum likelihood estimator) and a possibly biased but more efficient model-based estimator (e.g. distributed lagged model estimator) to enhance estimation efficiency without undermining much robustness via an optimal bias-variance tradeoff. The simulation results indicate that shrinkage-type estimators are more efficient when the specification of distributed lagged model is biased and the efficiency is comparable when the model-based estimator is nearly unbiased. We use National Morbidity, Mortality, and Air Pollution Study (NMMAPS) dataset to illustrate our methods. In general, the shrinkage-type approaches are advantageous in the scenario that none of the estimators are universally superior and can be applied in areas beyond environmental epidemiology.
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