Abstract:
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We propose a framework for flexibly modeling local dependence among variables having a known ordering. Our target of inference is the inverse of the Cholesky factor of the covariance matrix, which provides a simple interpretation for local dependence when only elements close to its diagonal are nonzero. The estimator is the solution to a convex, penalized Gaussian likelihood problem with a hierarchical group lasso penalty. The problem can be decomposed into independent subproblems which can be solved efficiently. Because of the convexity and decomposability of our formulation, the estimator has theoretical results that are not found in existing estimators attaining this structure. In particular, signed support recovery and estimation consistency in multiple norms are established. Empirical results show our estimator performing favorably compared to existing estimators. We apply our estimator to data from the HapMap project to flexibly model linkage disequilibrium.
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