<p>Consider a high-dimensional normal linear regression model when the candidate regressors are inherently grouped. Our interest is in grouped variable selection and estimation of parameters in a sparse asymptotic regime. We model the grouped regression coefficients by a broad class of “global–local" shrinkage priors which can also be seen as a generalization of the standard g-prior with a shrinkage parameter. The global shrinkage parameter is either treated as a tuning parameter or in an empirical Bayes estimator or full Bayesian way. We consider a group selection rule, namely the Half-Thresholding rule and an estimator using that. Our methods are to enjoy the oracle property asymptotically in that they achieve variable selection consistency and optimal rate of estimation under a block-orthogonal design. These are the first theoretical results of their kind using such priors in this context. In simulation study, our rules perform favorably to many existing methods.</p>