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Abstract:
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We consider penalized estimation in additive models with a large number of mixed components including univariate linear effects, group effects and nonparametric effects of one or several variables. A prediction error bound, derived under a restricted eigenvalue or compatibility condition, provides rate optimality for the penalized estimator in various settings. In nonparametric additive models, the prediction error bound yields existing and new results under different smoothness and sparsity conditions. An adaptive estimator is constructed to unify these and some non-convex rate optimal methods. This is joint work with Zhiqiang Tan.
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