Researchers have developed a new method for empirical Bayes estimation in correlated Gaussian sequence models. This approach utilizes a maximum Composite Marginal Likelihood (CML) estimator, which effectively handles dependent observations by ignoring correlations in the likelihood. The CML estimator demonstrates convergence at a rate of $n_*^{-1/2}$, where $n_*$ is the effective sample size, indicating near rate optimality under general dependence. The method is applied to Bayesian linear regression and Bayesian nonlinear single-index models, leveraging high-dimensional distributions of auxiliary statistics. AI
IMPACT This research advances statistical methods relevant to large-scale inference, potentially impacting AI model training and analysis.
RANK_REASON The cluster contains an academic paper detailing a new statistical method.
- Bayesian linear regression
- Bayesian nonlinear single-index model
- Brascamp-Lieb inequality
- Composite Marginal Likelihood
- Gaussian sequence model
- gradient descent
- Least Squares Estimator
- NPMLE
- Hellinger distance
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