Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Anomalies in the Foundations of Ridge Regression   Anomalies persist in the foundations of ridge regression as set forth in
Hoerl and Kennard (1970) and subsequently. Conventional ridge estimators and
their properties do not follow on constraining lengths of solution vectors
using LaGrange's method, as claimed. Estimators so constrained have singular
distributions; the proposed solutions are not necessarily minimizing; and
heretofore undiscovered bounds are exhibited for the ridge parameter. None of
the considerable literature on estimation, prediction, cross--validation,
choice of ridge parameter, and related issues, collectively known as ridge
regression, is consistent with constrained optimization, nor with corresponding
inequality constraints. The problem is traced to a misapplication of LaGrange's
principle, failure to recognize the singularity of distributions, and misplaced
links between constraints and the ridge parameter. Other principles, based on
condition numbers, are seen to validate both conventional ridge and surrogate
ridge regression to be defined. Numerical studies illustrate that ridge
analysis often exhibits some of the same pathologies it is intended to redress.

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The categories of this paper are: math-ph
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The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: nlin
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The categories of this paper are: funct-an
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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: gr-qc
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The categories of this paper are: cmp-lg
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ex
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The categories of this paper are: solv-int
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The categories of this paper are: q-alg