Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Smooth supersaturated models   In areas such as kernel smoothing and non-parametric regression there is
emphasis on smooth interpolation and smooth statistical models. Splines are
known to have optimal smoothness properties in one and higher dimensions. It is
shown, with special attention to polynomial models, that smooth interpolators
can be constructed by first extending the monomial basis and then minimising a
measure of smoothness with respect to the free parameters in the extended
basis. Algebraic methods are a help in choosing the extended basis which can
also be found as a saturated basis for an extended experimental design with
dummy design points. One can get arbitrarily close to optimal smoothing for any
dimension and over any region, giving a simple alternative models of spline
type. The relationship to splines is shown in one and two dimensions. A case
study is given which includes benchmarking against kriging methods.

36
The categories of this paper are: cmp-lg
2
The categories of this paper are: math
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th