@article{b955b484-65fd-422c-8e32-b31510d657df,
  abstract     = {{<p>We study variational shrinkage in the sparse normal means model and compare it with the corresponding exact Bayes shrinkage rule. The focus is on the excess quadratic risk of the variational posterior mean. Using a squared-loss decomposition, we show that this excess risk is bounded by the discrepancy between the variational and exact Bayes estimators together with the benchmark Bayes risk. This yields a simple criterion for asymptotic equivalence, since the two estimators have asymptotically the same quadratic risk whenever the variational shrinkage rule is sufficiently close to the exact Bayes rule. Simulations and a semi-synthetic Golub leukemia example illustrate how the risk gap behaves under exact sparsity, approximate sparsity, and real-data-derived sparse signals.</p>}},
  author       = {{Javed, Farrukh}},
  issn         = {{0167-7152}},
  keywords     = {{Bayes shrinkage; Excess risk; High-dimensional inference; Sparse normal means; Variational inference}},
  language     = {{eng}},
  publisher    = {{Elsevier}},
  series       = {{Statistics and Probability Letters}},
  title        = {{Variational shrinkage and excess risk in sparse normal means}},
  url          = {{http://dx.doi.org/10.1016/j.spl.2026.110846}},
  doi          = {{10.1016/j.spl.2026.110846}},
  volume       = {{238}},
  year         = {{2026}},
}