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Journal of Statistical Planning and Inference, ISSN 0378-3758, 2011, Volume 141, Issue 2, pp. 817 - 830
Local depth is a generalization of ordinary depth able to reveal local features of the probability distribution. Liu's simplicial depth is primarily used, but... 
Halfspace depth | Simplicial depth | Multimodal distribution | Data depth | TESTS | STATISTICS & PROBABILITY | U-PROCESSES
Journal Article
Journal Article
Discrete and Computational Geometry, ISSN 0179-5376, 07/2017, Volume 58, Issue 1, pp. 51 - 66
Journal Article
DISCRETE & COMPUTATIONAL GEOMETRY, ISSN 0179-5376, 07/2017, Volume 58, Issue 1, pp. 51 - 66
Journal Article
The Annals of Statistics, ISSN 0090-5364, 4/2000, Volume 28, Issue 2, pp. 461 - 482
Journal Article
Computational Statistics and Data Analysis, ISSN 0167-9473, 07/2016, Volume 99, pp. 235 - 247
At about the same time (approximately 1989), R. Liu introduced the notion of simplicial depth and R. Randles the notion of interdirections. These completely... 
Simplicial depth | Interdirections | Sign tests | Multivariate | Computational burden
Journal Article
Computational Statistics and Data Analysis, ISSN 0167-9473, 07/2016, Volume 99, pp. 235 - 247
Journal Article
Journal of Combinatorial Theory, Series A, ISSN 0097-3165, 02/2015, Volume 130, pp. 119 - 128
Given sets of points, or colours, in , a is a set such that for all . The colourful Carathéodory theorem states that, if is in the convex hull of each , then... 
Octahedral systems | Colourful simplicial depth | Colourful Carathéodory theorem | MATHEMATICS | Colourful Caratheodory theorem
Journal Article
ALEA-LATIN AMERICAN JOURNAL OF PROBABILITY AND MATHEMATICAL STATISTICS, ISSN 1980-0436, 2013, Volume 10, Issue 2, pp. 831 - 855
We study some problems inherent with certain forms of functional depth, in particular, zero depth and lack of consistency. 
simplicial depth | half-space depth | STATISTICS & PROBABILITY | CLT | consistency | functional depth
Journal Article
Journal of Time Series Analysis, ISSN 0143-9782, 11/2016, Volume 37, Issue 6, pp. 763 - 784
We propose outlier a robust and distribution‐free test for the explosive AR(1) model with intercept based on simplicial depth. In this model, simplicial depth... 
Alternating sign | consistency.JEL. 62M10 | distribution‐free test | simplicial depth | robustness | 62G10 | autoregression | 62G35 | 62F05 | distribution-free test | REGRESSION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ROBUST | ESTIMATORS | GROWTH | STATISTICS & PROBABILITY | consistency | Studies | Time series
Journal Article
SIAM Journal on Discrete Mathematics, ISSN 0895-4801, 2014, Volume 28, Issue 1, pp. 306 - 322
The colourful simplicial depth conjecture states that any point in the convex hull of each of d + 1 sets, or colours, of d + 1 points in general position in... 
Octahedral systems | Colourful Carathéodory theorem | Colourful simplicial depth | Realizability | MATHEMATICS, APPLIED | colourful Caratheodory theorem | colourful simplicial depth | octahedral systems | realizability
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 07/2013, Volume 141, Issue 7, pp. 2265 - 2274
Let I ⊂ S = 𝕂, [x 1 ,...,x n ] be an ideal generated by square-free monomials of degree ≥ d. If the number of degree d minimal generating monomials is... 
Squarefree monomial ideal | Stanley depth | MATHEMATICS | DECOMPOSITIONS | MATHEMATICS, APPLIED | squarefree monomial ideal | SIMPLICIAL COMPLEXES | MONOMIAL IDEALS
Journal Article
Archiv der Mathematik, ISSN 0003-889X, 1/2015, Volume 104, Issue 1, pp. 3 - 9
Recently, Seyed Fakhari proved that if I is a weakly polymatroidal monomial ideal in $${S\,=\,\mathbb{K}[x_1,\ldots,x_n]}$$ S = K [ x 1 , … , x n ] , then... 
Primary 05E40 | Vertex decomposable simplicial complex | Stanley depth | 13C40 | Mathematics, general | Mathematics | 05E45 | Secondary 13C14 | MATHEMATICS | MULTIGRADED MODULES
Journal Article
Journal of Multivariate Analysis, ISSN 0047-259X, 2010, Volume 101, Issue 10, pp. 2358 - 2371
Global depth, tangent depth and simplicial depths for classical and orthogonal regression are compared in examples, and properties that are useful for... 
Orthogonal regression | Simplicial depth | Tangent depth | Asymptotic tests | Global depth | TESTS | ESTIMATORS | STATISTICS & PROBABILITY | POLYNOMIAL REGRESSION | Orthogonal regression Tangent depth Global depth Simplicial depth Asymptotic tests | Algorithms | Studies | Regression analysis | Estimating techniques | Simulation
Journal Article
Mathematische Nachrichten, ISSN 0025-584X, 08/2015, Volume 288, Issue 11-12, pp. 1360 - 1370
Let J ⊈ I be two monomial ideals of the polynomial ring S = K [ x 1 , ... , x n ] . In this paper, we provide two lower bounds for the Stanley depth of I / J .... 
Monomial ideal | lcm number | Primary: 13C15 | Stanley depth | lcm lattice | order dimension | simplicial complex | 05E99 | Secondary: 13C13 | Lcm lattice | Order dimension | Simplicial complex | Lcm number | MATHEMATICS | DECOMPOSITIONS | SIMPLICIAL COMPLEXES | RESOLUTIONS | Heuristic
Journal Article
Archiv der Mathematik, ISSN 0003-889X, 10/2012, Volume 99, Issue 4, pp. 315 - 325
We extend a result of Minh and Trung (Adv. Math. 226:1285–1306, 2011) to get criteria for depth $${I = \rm {depth}\sqrt{I}}$$ , where I is an unmixed monomial... 
Mathematics, general | 13D45 | Stanley–Reisnerrings | Mathematics | Monomial ideals | Simplicial complexes | Primary 13C15 | Depth | Secondary 13F55 | Stanley-Reisnerrings | MATHEMATICS | Stanley-Reisner rings
Journal Article
Journal of Algebra, ISSN 0021-8693, 04/2016, Volume 452, pp. 157 - 187
Let be a graph and let be its edge ideal. In this paper, we provide an upper bound of from which is stationary, and compute this limit explicitly. This bound... 
Monomial ideal | Stanley–Reisner ideal | Graph | Edge ideal | Simplicial complex | Depth | Stanley-Reisner ideal | MATHEMATICS | STABLE SET | STANLEY-REISNER IDEALS | COHEN-MACAULAYNESS
Journal Article
Journal of Statistical Planning and Inference, ISSN 0378-3758, 09/2012, Volume 142, Issue 9, pp. 2501 - 2517
In this paper it is shown that data depth does not only provide consistent and robust estimators but also consistent and robust tests. Thereby, consistency of... 
Consistency | Gumbel copula | Robustness | Simplicial depth | Likelihood depth | Parametric estimation | Weibull distribution | Breakdown point | Data depth | Gaussian copula | Tests | STATISTICS & PROBABILITY | POLYNOMIAL REGRESSION | STATISTICAL DEPTH | POINTS
Journal Article
Journal Article
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