«ZONOID»に関連する英語の本
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1
Multivariate Dispersion, Central Regions, and Depth: The ...
This book introduces a new representation of probability measures, the lift zonoid representation, and demonstrates its usefulness in statistical applica tions.
2
Data Depth: Robust Multivariate Analysis, Computational ...
and Theoretical Computer Science Volume 72, 2006 Data analysis and
classification with the zonoid depth Karl Mosler and Richard Hoberg ABSTRACT.
The zonoid depth is useful in multivariate data analysis in order to describe an
empirical ...
Regina Y. Liu, Robert Joseph Serfling, Diane L. Souvaine
3
COMPSTAT: Proceedings in Computational Statistics ; 14th ...
Rainer Dyckerhoff Seminar fur Wirtschafts- und Sozialstatistik, Universitat zu Koln
, 50923 Koln, Germany Keywords. Multivariate trimming, algorithm, zonoid depth,
convex sets 1 Introduction In data analyis an important task is to identify sets of ...
Jelke G. Bethlehem, Peter G.M. van der Heijden, 2000
4
Soft Methodology and Random Information Systems
The zonoid trimmed regions induce the zonoid depth function that assigns to
each x € Rd the value ZD(x; F) := sup{a e (0, 1] : z € ZDa(F)}. The depth of a point
measures its centrality with respect to a probability distribution. For the zonoid
depth ...
5
Papers in Algebra, Analysis, and Statistics
It is clear from the definition that the sum of /c-zonoids is a k-zonoid and that the
affine image of a fe-zonoid is a fe-zonoid. o Every compact convex set in IR with a
centre of symmetry is a 1-zonoid (see for example [3]). It is also known that every
...
The measure μ of the previous theorem is called the generating measure of the
zonoid K. It is essentially unique, by Theorem C.2.1. Theorem 4.1.11. A projection
body is a centered zonoid. Conversely, every centered n-dimensional zonoid in ...
7
Convex Bodies: The Brunn–Minkowski Theory
El We collect some consequences of these and former observations. Corollary
3.5.7 Every support set of a generalized zonoid is itself a generalized zonoid and
is, in particular, centrally symmetric. Every support set of a zonoid is a summand ...
8
Advances in Theoretical and Applied Statistics
By resorting both to multiple linear regression model and Lorenz zonoid tools,
one obtains LZ(Y) 20.245, LZ(YYJgO-Om, LzdkQgonos and LZ(ikhX-J'gO-054.
Through (Q) and (Q), the following single partial dependence measures can be ...
Nicola Torelli, Fortunato Pesarin, Avner Bar-Hen, 2013
9
Stochastic and Integral Geometry
We put ΠX := Πd−1(γQ) and call Π X the associated zonoid of the hyperplane
process X. By (4.58), we have h(ΠX,u) = γ2 ∫ Sd−1 |〈u,v〉|φ(dv), u∈Rd, (4.59)
where φ is the spherical directional distribution of X. According to Theorem 14.3.4
, ...
Rolf Schneider, Wolfgang Weil, 2008
Definition 1.14 (Zonoid and lift zonoid of a random vector). Let ξ be a random
vector in Rd. Its zonoid, Zξ, is the selection expectation of X = {0,ξ}. The lift zonoid,
̃Zξ, of ξ is the selection expectation of the segment in Rd+1 with the endpoints ...
