Tukey depth: linear programming and applications arXiv
29 февр. 2016 г. Keywords: Tukey depth; Linear programming; Cone segmentation; Breadth- first search algorithm; Exact computation; Simplex algorithm. 1 ...
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An Optimal Randomized Algorithm for Maximum Tukey Depth
We are interested in finding a Tukey median that is
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On Generalization and Computation of Tukeys Depth: Part I
1 июл. 2021 г. 2018; Gao 2020) Tukey-type depths suffer some serious issues that hinder their usage in real-life multivariate data. Perhaps the biggest ...
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A Simple Heuristic for the Graph Tukey Depth Problem with Potential
Abstract. We study a recently introduced adaptation of Tukey depth to graphs and discuss its algorithmic properties and potential applications to mining and
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Exact computation of the halfspace depth arXiv:1411.6927v3 [stat
12 янв. 2016 г. Keywords: Tukey depth; Exact algorithm; Projection; Combinatorial algorithm; Orthogonal complement. 1 Introduction. In 1975 John W. Tukey ...
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Tukeys Depth for Object Data
1 сент. 2021 г. For multivariate Euclidean data Tukey's halfspace depth (Tukey
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Some intriguing properties of Tukeys half-space depth
5 янв. 2012 г. The Tukey median the multivariate median associated with the half-space depth
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Asymptotics for the Tukey Depth Process with an Application to a
Tukey depth process and that of the empirical simplicial depth process. For any F it is known that the latter is asymptotically Gaussian (Arcones and Gin6
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The Tukey Depth Characterizes the Atomic Measure
12 февр. 2002 г. depth we will call it the Tukey depth. In detail
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On the quality of randomized approximations of Tukeys depth arXiv
20 окт. 2023 г. Abstract. Tukey's depth (or halfspace depth) is a widely used measure of centrality for multivariate data. However exact computation of ...
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Tukey depth: linear programming and applications arXiv
Feb 29 2016 Here the issue of exact computation of the classical Tukey data depth is addressed. The paper suggests an algo- rithm that exploits connection ...
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Estimating Tukey Depth Using Incremental Quantile Estimators arXiv
Jan 8 2020 The suggested algorithm can estimate depth contours when the dataset in known in advance
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Tukeys Depth for Object Data
Sep 1 2021 For multivariate Euclidean data
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Output-Sensitive Algorithms for Tukey Depth and Related Problems
Keywords: Tukey depth halfspace depth
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Concentration of the empirical level sets of Tukeys halfspace depth
Abstract: Tukey's halfaspace depth has attracted much interest in data analysis because it is a natural way of measuring the notion of depth.
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The Random Tukey Depth
Jan 28 2008 Key words and phrases: Random Tukey depth
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On Generalization and Computation of Tukeys Depth: Part I
Jul 1 2021 Keywords: Tukeyfication
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An Optimal Randomized Algorithm for Maximum Tukey Depth
We are interested in finding a Tukey median that is
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58 COMPUTATION OF ROBUST STATISTICS: DEPTH MEDIAN
Tukey median: Median based on halfspace depth. HALFSPACE LOCATION DEPTH. Let Xn = {x1
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Fast computation of Tukey trimmed regions and median in
Nov 8 2018 To calculate the Tukey depth d(x
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On Generalization and Computation of Tukey’s Depth: Part I
Tukey’s depth o?ers a powerful tool for nonparametric inference andestimationbutalsoencountersseriouscomputationalandmethod-ological di?culties in modern statistical data analysis This paper studies how to generalize and compute Tukey-type depths in multi-dimensions A general framework of in?uence-driven polished sub-
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The following data (in increasing order) for the attribute age: 13 15
IfPis absolutely continuous the Tukey depth is a continuous functionof zachieving maximum value of 1 for angularly symmetric distributions at 2 the center of symmetry IfPhas no Lebesgue density the Tukey depth is adiscrete function of zand can have a non-unique maximum
Jan 22 2022 · File:Tukey's halfspace depth pdf From Wikimedia Commons the free media repository File File history File usage on Commons File usage on other wikis Metadata Size of this JPG preview of this PDF file: 627 × 599 pixels Other resolutions: 251 × 240 pixels 502 × 480 pixels 803 × 768 pixels 1229 × 1175 pixels
What is the Tukey method?
The Tukey method: Calculate the data's interquartile range (IQR), and consider any data point that is more than 1.5 times the IQR below or above the first quartile to be an outlier. Visual examination: Plot the data and look for any values that seem out of place with the rest of the data.
What is the significance level of the Tukey procedure?
For example, when using the Tukey procedure with a significance level of, say, 5%, we are assured that there is at most a 5% chance of obtaining a false positive among the entire set of pairwise tests, That is, there is at most a 5% chance of mistakenly concluding that two population means differ when, in fact, they are equal.
What is the Tukey outer fence methodology?
Building on past comments, CMS proposes to use a statistical methodology known as the Tukey outer fence methodology to identify and delete outliers.
What are the different editions of Tukey's exploratory data analysis?
Exploratory Data Analysis 1 (limited preliminary edition). Addison-Wesley, Reading, MA. TUKEY, J. W. (1970d). Exploratory Data Analysis 2 (limited preliminary edition). Addison-Wesley, Reading, MA. TUKEY, J. W. (1971a).
Approximate Calculation of Tukeys Depth and Median With High
Using different versions of this algorithm, we demonstrate ap- proximate calculations of the deepest set of points (”Tukey median”) and Tukey's depth of a sample
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The Random Tukey Depth - Universidad de Cantabria
28 jan 2008 · The computation of the Tukey depth, also called halfspace depth, is very demanding, even in low dimensional spaces, because it requires that
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OUTPUT-SENSITIVE ALGORITHMS FOR TUKEY DEPTH AND
The Tukey depth (Tukey 1975) of a point p with respect to a finite set S of points is the minimum number of elements of S contained in any closed halfspace that
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An Optimal Randomized Algorithm for Maximum Tukey Depth
We are interested in finding a Tukey median, that is, a point q ∈ IRd with the largest Tukey depth 1 2 Motivation Notions of depths for point data sets are important
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Contributions to depth-based classification and - Universität zu Köln
viding their paper on exact computation of the Tukey depth with the Matlab source code of the algorithm I am grateful to Robert Jumpertz and Holger
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The Concept of Depth In Statistics
The notion of data depth was proposed by Tukey (1975) as a graphical tool for visualizing bivariate data sets, and has since been extended to the multivariate
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[PDF] An Optimal Randomized Algorithm for Maximum Tukey Depth
The above definition (also called location depth, data depth, and halfspace depth) is among the most well known and was popularized by John Tukey [47], who suggested using the corresponding depth contours (boundaries of regions of all points with equal depth) to visualize data
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[PDF] The Concept of Depth In Statistics
Since 1975, when Tukey (1975) introduced the location depth, many more depth functions have been pro posed Some of these functions are defined in Section 2 Most depth functions are robust and affine invariant making them well suited for the study of real life high dimensional data sets that may contain outliers
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[PDF] approximate calculation of tukeys depth and median with high
In this paper we propose an algo rithm for halfspace depth (Tukey's depth, [31]), which is based on extension and generalization of (2) to Rd with balls in place of
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[PDF] Absolute Approximation of Tukey Depth - Computational Geometry
Feb 29, 2012 · Introduction Tukey depth is also known as location depth or halfspace depth Given a finite set S of n points and a point p in Rd, the Tukey
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[PDF] Some Extensions of Tukeys Depth Function - Semantic Scholar
than that based on Tukey's depth The dispersion depth functions provide some additional view of the dispersion of the data set It is shown that these sample
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[PDF] Some Extensions of Tukeys Depth Function - Eurandom
than that based on Tukey's depth The dispersion depth functions provide some additional view of the dispersion of the data set It is shown that these sample
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[PDF] 58 computation of robust statistics: depth, median, and - CSUNedu
Tukey median Median based on halfspace depth HALFSPACE LOCATION DEPTH Let Xn = {x1,, xn} be a finite set of data points
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[PDF] Package depth - CRAN
Nov 21, 2019 · Function depth calculates the depth of a point with respect to the data set Depth functions covered are Tukey's, Liu's and Oja's Functions
random tukey depth
turkey half space depth
PDF) Tukey depth: linear programming and applications
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