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2002, Lecture notes in statistics, ISBN 0387954120, Volume 165, x, 291
Book
Statistical Papers, ISSN 0932-5026, 2/2014, Volume 55, Issue 1, pp. 49 - 69
Journal Article
Statistics and Probability Letters, ISSN 0167-7152, 03/2019, Volume 146, pp. 70 - 79
In this paper, we point out a common feature of zonoid and empirical depths that gives rise to a novel class of data depths, and provide a possible... 
Weighted mean | Zonoid depth | Weighted zonoid depth | General empirical depth | PROJECTION DEPTH | CLASSIFICATION | STATISTICS & PROBABILITY
Journal Article
Applied Mathematical Modelling, ISSN 0307-904X, 01/2018, Volume 53, pp. 487 - 509
Journal Article
Journal of Multivariate Analysis, ISSN 0047-259X, 01/2016, Volume 143, pp. 394 - 397
Under some mild conditions on probability distribution , if weakly then the sequence of zonoid depth functions with respect to converges uniformly to the... 
Zonoid depth | Uniform consistency | STATISTICS & PROBABILITY | Studies | Probability distribution | Mathematical functions | Vector space
Journal Article
Computational Geometry: Theory and Applications, ISSN 0925-7721, 2008, Volume 39, Issue 1, pp. 2 - 13
Zonoid depth is a definition of data depth proposed by Dyckerhoff et al. [R. Dyckerhoff, G. Koshevoy, K. Mosler, Zonoid data depth: Theory and computation, in:... 
Statistical data depth | Zonotopes | Zonoids | zonotopes | MATHEMATICS | MATHEMATICS, APPLIED | zonoids | statistical data depth | PLANAR SET | OPTIMIZATION | POINTS | LINES | Computer science | Algorithms
Journal Article
Journal of Multivariate Analysis, ISSN 0047-259X, 05/2012, Volume 107, pp. 306 - 318
Journal Article
Computational Geometry: Theory and Applications, ISSN 0925-7721, 2008, Volume 39, Issue 3, pp. 229 - 235
A randomized linear expected-time algorithm for computing the zonoid depth [R. Dyckerhoff, G. Koshevoy, K. Mosler, Zonoid data depth: Theory and computation,... 
Robust statistics | Support vector machines | Zonotopes | Data depth | Zonoids | zonotopes | LINEAR-TIME | MATHEMATICS | O(N) ALGORITHM | MATHEMATICS, APPLIED | data depth | support vector machines | DIMENSION | zonoids | robust statistics | Computer science | Algorithms
Journal Article
Journal of Multivariate Analysis, ISSN 0047-259X, 2011, Volume 102, Issue 3, pp. 405 - 421
Journal Article
Journal of Multivariate Analysis, ISSN 0047-259X, 2005, Volume 96, Issue 2, pp. 404 - 424
We define a new family of central regions with respect to a probability measure. They are induced by a set or a family of sets of functions and we name them .... 
Depth function | Halfspace trimming | Trimmed region | Zonoid trimming | DISTRIBUTIONS | RANDOM VECTORS | depth functions | trimmed region | halfspace trimming | GLIVENKO-CANTELLI | NOTIONS | STATISTICS & PROBABILITY | STATISTICAL DEPTH FUNCTIONS | zonoid trimming | Depth function Halfspace trimming Trimmed region Zonoid trimming | Studies | Probability
Journal Article
METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY, ISSN 1387-5841, 03/2003, Volume 5, Issue 1, pp. 5 - 21
The paper introduces an approach to the ordering of dependence which is based on central regions. A d-variate probability distribution is described by a nested... 
trimmed regions | dependence order | generalized correlation | data depth | NOTIONS | STATISTICS & PROBABILITY | lift zonoid volume | DEPTH | RANK-TESTS | Studies | Probability | Mathematical analysis
Journal Article
Methodology And Computing In Applied Probability, ISSN 1387-5841, 3/2003, Volume 5, Issue 1, pp. 5 - 21
The paper introduces an approach to the ordering of dependence which is based on central regions. A d-variate probability distribution is described by a nested... 
trimmed regions | dependence order | Economics general | generalized correlation | data depth | Life Sciences, general | Statistics, general | Business/Management Science, general | Statistics | lift zonoid volume | Electronic and Computer Engineering
Journal Article
Statistics and Probability Letters, ISSN 0167-7152, 02/2019, Volume 145, pp. 110 - 117
It is known that the distribution of an integrable random vector in is uniquely determined by a -dimensional convex body called the lift zonoid of . This... 
Outlier | Lift zonoid | Support function | Risk measure | Selection expectation | Random set | CONVEX HULLS | STATISTICS & PROBABILITY | ZONOIDS
Journal Article
Bernoulli, ISSN 1350-7265, 2014, Volume 20, Issue 3, pp. 1210 - 1233
Two integrable random vectors xi and xi* in R-d are said to be zonoid equivalent if, for each u is an element of R-d, the scalar products and Ergodic theorem | Swap-invariance | Isometry | Zonoid | Exchangeability | SPECTRAL REPRESENTATION | FIELDS | exchangeability | PRICES | PUT-CALL SYMMETRY | ergodic theorem | swap-invariance | STATISTICS & PROBABILITY | MAX-STABLE PROCESSES | zonoid | isometry | Mathematics - Probability
Journal Article
Theory of Probability and Mathematical Statistics, ISSN 0094-9000, 2014, Volume 89, pp. 83 - 99
We introduce the notion of a weighted lift zonoid, and we show that the ordering condition imposed on a measure \mu such as non-linear extensions of Bobkov's... 
Lift zonoid | Log-Sobolev inequality | Shift inequality | Weight
Journal Article
Statistics and Probability Letters, ISSN 0167-7152, 2012, Volume 82, Issue 2, pp. 318 - 325
In this paper we investigate a new class of central regions for probability distributions on , called weighted-mean regions. Their restrictions to an empirical... 
Central regions | Lift zonoid regions | Expected convex hull | Continuous trimming | Variability order | SAMPLE | STATISTICS & PROBABILITY
Journal Article
Advances in Mathematics, ISSN 0001-8708, 2010, Volume 225, Issue 4, pp. 1914 - 1928
A stability version of the Blaschke–Santaló inequality and the affine isoperimetric inequality for convex bodies of dimension is proved. The first step is the... 
Affine invariant inequalities | Stability | MATHEMATICS | SURFACE-AREA | CONVEX-BODIES | MINIMAL VOLUME-PRODUCT | ELLIPSOIDS | BODY | ZONOIDS | Equality
Journal Article
SIAM Journal on Optimization, ISSN 1052-6234, 2006, Volume 16, Issue 4, pp. 1024 - 1043
Journal Article
The Journal of Economic Inequality, ISSN 1569-1721, 1/2005, Volume 2, Issue 2, pp. 89 - 103
Journal Article
The Journal of Economic Inequality, ISSN 1569-1721, 8/2004, Volume 2, Issue 2, pp. 89 - 103
Journal Article
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