The proposed hierarchical Beta (Polya tree) posterior mean achieves lower mean squared error than MLE, Lasso, ridge, and adjusted MLE in three simulated high-dimensional logistic regression settings.
On F-Modelling based Empirical Bayes Estimation of Variances
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abstract
We consider the problem of empirical Bayes estimation of multiple variances when provided with sample variances. Assuming an arbitrary prior on the variances, we derive different versions of the Bayes estimators using different loss functions. For one particular loss function, the resulting Bayes estimator relies on the marginal cumulative distribution function of the sample variances only. When replacing it with the empirical distribution function, we obtain an empirical Bayes version called F-modeling based empirical Bayes estimator of variances. We provide theoretical properties of this estimator and further demonstrate its advantages through extensive simulations and real data analysis.
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stat.ME 1years
2019 1verdicts
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Nonparametric Shrinkage Estimation in High Dimensional Generalized Linear Models via Polya Trees
The proposed hierarchical Beta (Polya tree) posterior mean achieves lower mean squared error than MLE, Lasso, ridge, and adjusted MLE in three simulated high-dimensional logistic regression settings.