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 achieves a convergence rate of $n_*^{-1/2}$, where $n_*$ is the effective sample size, demonstrating near rate optimality under general dependence conditions. The method has been 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 potentially applicable to large-scale inference in AI, particularly in areas involving correlated data.
RANK_REASON The item is an academic paper detailing a new statistical method. [lever_c_demoted from research: ic=1 ai=0.4]
- Bayesian linear regression
- Bayesian nonlinear single-index model
- Brascamp-Lieb inequality
- Composite Marginal Likelihood
- Gaussian sequence model
- gradient descent
- Least Squares Estimator
- NPMLE
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