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

Halfspace depth | Simplicial depth | Multimodal distribution | Data depth | TESTS | STATISTICS & PROBABILITY | U-PROCESSES

Journal Article

Journal of the American Statistical Association, ISSN 0162-1459, 06/1999, Volume 94, Issue 446, pp. 388 - 402

In this article we introduce a notion of depth in the regression setting. It provides the "rank" of any line (plane), rather than ranks of observations or...

Geometry | Asymmetric error distribution | Depth quantiles | Depth envelopes | Halfspace depth | Simplicial depth | Robust regression | Deepest regression | Heteroscedasticity | Datasets | Statistical median | Mathematical theorems | Theory and Methods | Linear regression | Statistical theories | Hyperplanes | Data lines | Contour lines | Estimators | Parallel lines | deepest regression | heteroscedasticity | depth quantiles | asymmetric error distribution | simplicial depth | depth envelopes | robust regression | LOCATION DEPTH | STATISTICS & PROBABILITY | geometry | halfspace depth | Regression analysis | Research | Multivariate analysis | Estimation theory

Geometry | Asymmetric error distribution | Depth quantiles | Depth envelopes | Halfspace depth | Simplicial depth | Robust regression | Deepest regression | Heteroscedasticity | Datasets | Statistical median | Mathematical theorems | Theory and Methods | Linear regression | Statistical theories | Hyperplanes | Data lines | Contour lines | Estimators | Parallel lines | deepest regression | heteroscedasticity | depth quantiles | asymmetric error distribution | simplicial depth | depth envelopes | robust regression | LOCATION DEPTH | STATISTICS & PROBABILITY | geometry | halfspace depth | Regression analysis | Research | Multivariate analysis | Estimation theory

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

Let X be a finite set of points in R-d. The Tukey depth of a point q with respect to X is the minimum number tau(X) (q) of points of X in a halfspace...

COLORFUL | MATHEMATICS | SIMPLICES | Helly type theorem | CONVEX-BODIES | COMPUTER SCIENCE, THEORY & METHODS | Tukey depth | Simplicial depth | GEOMETRY | 32F Geometric convexity | Teoremes | Anàlisi matemàtica | Convex geometry | Matemàtiques i estadística | Classificació AMS | 32 Several complex variables and analytic spaces | Àrees temàtiques de la UPC

COLORFUL | MATHEMATICS | SIMPLICES | Helly type theorem | CONVEX-BODIES | COMPUTER SCIENCE, THEORY & METHODS | Tukey depth | Simplicial depth | GEOMETRY | 32F Geometric convexity | Teoremes | Anàlisi matemàtica | Convex geometry | Matemàtiques i estadística | Classificació AMS | 32 Several complex variables and analytic spaces | Àrees temàtiques de la UPC

Journal Article

The Annals of Statistics, ISSN 0090-5364, 4/2000, Volume 28, Issue 2, pp. 461 - 482

Statistical depth functions are being formulated ad hoc with increasing popularity in nonparametric inference for multivariate data. Here we introduce several...

Datasets | Data Depth | Maximality | Infinity | Random sampling | Statistical theories | Inference | Mathematical functions | Convexity | Covariance matrices | Estimators | Halfspace depth | Simplicial depth | Statistical depth functions | Multivariate symmetry | multivariate symmetry | LOCATION DEPTH | STATISTICS & PROBABILITY | halfspace depth | REGRESSION DEPTH | INFERENCE | BREAKDOWN POINT | DISTRIBUTIONS | statistical depth functions | simplicial depth | MULTIVARIATE-ANALYSIS | HALF-SPACE DEPTH | AGGREGATION | 62H05 | 62G20

Datasets | Data Depth | Maximality | Infinity | Random sampling | Statistical theories | Inference | Mathematical functions | Convexity | Covariance matrices | Estimators | Halfspace depth | Simplicial depth | Statistical depth functions | Multivariate symmetry | multivariate symmetry | LOCATION DEPTH | STATISTICS & PROBABILITY | halfspace depth | REGRESSION DEPTH | INFERENCE | BREAKDOWN POINT | DISTRIBUTIONS | statistical depth functions | simplicial depth | MULTIVARIATE-ANALYSIS | HALF-SPACE DEPTH | AGGREGATION | 62H05 | 62G20

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

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

At about the same time (approximately 1989), R. Liu introduced the notion of simplicial depth and R. Randles the notion of interdirections. These completely...

Interdirections | Sign tests | Simplicial depth | Multivariate | Computational burden | TESTS | LOCATION PROBLEM | STATISTICS & PROBABILITY | U-PROCESSES | INFERENCE | AFFINE-INVARIANT | SIGN TEST | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | LIMIT-THEOREMS | PSEUDO-MAHALANOBIS RANKS | STATISTICAL DEPTH | Reduction | Computation | Data processing | Case depth | Multivariate analysis | Statistical tests | Statistics

Interdirections | Sign tests | Simplicial depth | Multivariate | Computational burden | TESTS | LOCATION PROBLEM | STATISTICS & PROBABILITY | U-PROCESSES | INFERENCE | AFFINE-INVARIANT | SIGN TEST | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | LIMIT-THEOREMS | PSEUDO-MAHALANOBIS RANKS | STATISTICAL DEPTH | Reduction | Computation | Data processing | Case depth | Multivariate analysis | Statistical tests | Statistics

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

Octahedral systems | Colourful simplicial depth | Colourful Carathéodory theorem | MATHEMATICS | Colourful Caratheodory theorem

Journal Article

Advances in Data Analysis and Classification, ISSN 1862-5347, 9/2014, Volume 8, Issue 3, pp. 321 - 338

We propose notions of simplicial band depth for multivariate functional data that extend the univariate functional band depth. The proposed simplicial band...

Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences | 62M10 | Band depth | 62F07 | Statistics for Life Sciences, Medicine, Health Sciences | Functional boxplot | Data Mining and Knowledge Discovery | Modified band depth | Statistical Theory and Methods | Functional and image data | Statistics | Statistics for Business/Economics/Mathematical Finance/Insurance | Simplicial | Multivariate | Statistics for Social Science, Behavorial Science, Education, Public Policy, and Law | STATISTICS & PROBABILITY | CROSS-COVARIANCE FUNCTIONS

Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences | 62M10 | Band depth | 62F07 | Statistics for Life Sciences, Medicine, Health Sciences | Functional boxplot | Data Mining and Knowledge Discovery | Modified band depth | Statistical Theory and Methods | Functional and image data | Statistics | Statistics for Business/Economics/Mathematical Finance/Insurance | Simplicial | Multivariate | Statistics for Social Science, Behavorial Science, Education, Public Policy, and Law | STATISTICS & PROBABILITY | CROSS-COVARIANCE FUNCTIONS

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

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

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

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

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

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

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

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

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

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

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

Environmental and Ecological Statistics, ISSN 1352-8505, 6/2013, Volume 20, Issue 2, pp. 253 - 270

Data depth is a statistical method whose primary aim is to order data of a reference space according to centrality. This is particularly appealing for...

Life Sciences | Tukey’s depth | Mathematical and Computational Biology | Angular median | Bootstrap | Ecology | Depth regions | Statistics, general | Depth-based measures of dispersion | Simplicial depth | Evolutionary Biology | Tukey's depth | LOCATION | MULTIVARIATE | STATISTICS & PROBABILITY | RANDOM SIMPLICES | CIRCULAR DATA | DISTRIBUTIONS | ENVIRONMENTAL SCIENCES | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ESTIMATORS | MEDIANS | Environment | Bootstrap method | Statistical analysis | Skewed distributions | Summaries | Statistical methods | Dispersions | Order disorder | Statistics | Standards

Life Sciences | Tukey’s depth | Mathematical and Computational Biology | Angular median | Bootstrap | Ecology | Depth regions | Statistics, general | Depth-based measures of dispersion | Simplicial depth | Evolutionary Biology | Tukey's depth | LOCATION | MULTIVARIATE | STATISTICS & PROBABILITY | RANDOM SIMPLICES | CIRCULAR DATA | DISTRIBUTIONS | ENVIRONMENTAL SCIENCES | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ESTIMATORS | MEDIANS | Environment | Bootstrap method | Statistical analysis | Skewed distributions | Summaries | Statistical methods | Dispersions | Order disorder | Statistics | Standards

Journal Article

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