Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A geometrically motivated parametric model in manifold estimation,   The general aim of manifold estimation is reconstructing, by statistical
methods, an $m$-dimensional compact manifold $S$ on ${\mathbb R}^d$ (with
$m\leq d$) or estimating some relevant quantities related to the geometric
properties of $S$. We will assume that the sample data are given by the
distances to the $(d-1)$-dimensional manifold $S$ from points randomly chosen
on a band surrounding $S$, with $d=2$ and $d=3$. The point in this paper is to
show that, if $S$ belongs to a wide class of compact sets (which we call \it
sets with polynomial volume\rm), the proposed statistical model leads to a
relatively simple parametric formulation. In this setup, standard methodologies
(method of moments, maximum likelihood) can be used to estimate some
interesting geometric parameters, including curvatures and Euler
characteristic. We will particularly focus on the estimation of the
$(d-1)$-dimensional boundary measure (in Minkowski's sense) of $S$.
  It turns out, however, that the estimation problem is not straightforward
since the standard estimators show a remarkably pathological behavior: while
they are consistent and asymptotically normal, their expectations are infinite.
The theoretical and practical consequences of this fact are discussed in some
detail.

27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org