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Abstract:
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Many frequentist parametric statistical methods have large sample Bayesian analogs. However, there is no general Bayesian analog of "robust" covariance estimates, that are widely-used in frequentist work. We propose such an analog, produced as the Bayes rule under a form of balanced loss function, that combines elements of standard parametric inference with fidelity of the data to the model. Besides being the large-sample equivalent of its frequentist counterpart, we show by simulation that the Bayesian robust standard error can also be used to construct Wald confidence intervals that improve small-sample coverage.
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