Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Minimax Optimal Estimation in Partially Linear Additive Models under
  High Dimension   In this paper, we derive minimax rates for estimating both parametric and
nonparametric components in partially linear additive models with high
dimensional sparse vectors and smooth functional components. The minimax lower
bound for Euclidean components is the typical sparse estimation rate that is
independent of nonparametric smoothness indices. However, the minimax lower
bound for each component function exhibits an interplay between the
dimensionality and sparsity of the parametric component and the smoothness of
the relevant nonparametric component. Indeed, the minimax risk for smooth
nonparametric estimation can be slowed down to the sparse estimation rate
whenever the smoothness of the nonparametric component or dimensionality of the
parametric component is suffciently large. In the above setting, we demonstrate
that penalized least square estimators can nearly achieve minimax lower bounds.

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The categories of this paper are: patt-sol
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The categories of this paper are: cs
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The categories of this paper are: q-fin
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-ex
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The categories of this paper are: econ
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The categories of this paper are: cmp-lg
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The categories of this paper are: supr-con
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: quant-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: math-ph