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Characterization and Estimation of High-Dimensional Sparse Gaussian Regression Parameters Under Closed Polyhedral Cone Constraints (309923)

Keywords: Linear constraints, sparsity, shrinkage, high dimension, Bayesian lasso

We consider estimation of parameters in a high dimensional Gaussian regression setting where the parameters belong to a closed polyhedral cone. The polyhedral cones are defined as the solution set of a homogeneous set of linear inequalities. A special case is when the number of restrictions maybe higher than the number of parameters. One such situation arises in estimation of monotone curve using a non-parametric approach e.g., splines. In these high dimensional problems, one usually seeks a `sparse' solution. We define a notion of sparsity for such conic restrictions using lower dimensional facets of the cone. We also propose a sparse estimator of the constrained parameter vector by invoking a continuous shrinkage prior through the higher dimensional non-negative orthant representation of the polyhedral cone.