Bayesian sparse projection posteriors for high-dimensional grouped regression achieve optimal contraction rates and model selection consistency with applications to additive models and neuroimaging.
Lemma 7(Lemma 1 of Pal and Ghoshal [2024]).Under Assumption 3.3, max j=1,...,n 1− d2 j d2 j +a n = max j=1,...,n an d2 j +a n =o(n −1), whered 1
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Bayesian High-dimensional Grouped-regression using Sparse Projection-posterior
Bayesian sparse projection posteriors for high-dimensional grouped regression achieve optimal contraction rates and model selection consistency with applications to additive models and neuroimaging.