Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Model-free Envelope Dimension Selection   An envelope is a targeted dimension reduction subspace for simultaneously
achieving dimension reduction and improving parameter estimation efficiency.
While many envelope methods have been proposed in recent years, all envelope
methods hinge on the knowledge of a key hyperparameter, the structural
dimension of the envelope. How to estimate the envelope dimension consistently
is of substantial interest from both theoretical and practical aspects.
Moreover, very recent advances in the literature have generalized envelope as a
model-free method, which makes selecting the envelope dimension even more
challenging. Likelihood-based approaches such as information criteria and
likelihood-ratio tests either cannot be directly applied or have no theoretical
justification. To address this critical issue of dimension selection, we
propose two unified approaches -- called FG and 1D selections -- for
determining the envelope dimension that can be applied to any envelope models
and methods. The two model-free selection approaches are based on the two
different envelope optimization procedures: the full Grassmannian (FG)
optimization and the 1D algorithm (Cook and Zhang, 2016), and are shown to be
capable of correctly identifying the structural dimension with a probability
tending to 1 under mild moment conditions as the sample size increases. While
the FG selection unifies and generalizes the BIC and modified BIC approaches
that existing in the literature, and hence provides the theoretical
justification of them under weak moment condition and model-free context, the
1D selection is computationally more stable and efficient in finite sample.
Extensive simulations and a real data analysis demonstrate the superb
performance of our proposals.

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The categories of this paper are: eess
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The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-th
2
The categories of this paper are: math
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The categories of this paper are: chem-ph
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The categories of this paper are: adap-org
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: econ
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The categories of this paper are: math-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: comp-gas
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The categories of this paper are: physics
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The categories of this paper are: mtrl-th