Journal articles: 'Multivariate depth'

1

Bern and Eppstein. "Multivariate Regression Depth." Discrete & Computational Geometry 28, no. 1 (July 2002): 1–17. http://dx.doi.org/10.1007/s00454-001-0092-1.

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Claeskens, Gerda, Mia Hubert, Leen Slaets, and Kaveh Vakili. "Multivariate Functional Halfspace Depth." Journal of the American Statistical Association 109, no. 505 (January 2, 2014): 411–23. http://dx.doi.org/10.1080/01621459.2013.856795.

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Vencálek, Ondřej. "Depth-based Classification for Multivariate Data." Austrian Journal of Statistics 46, no. 3-4 (April 12, 2017): 117–28. http://dx.doi.org/10.17713/ajs.v46i3-4.677.

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Concept of data depth provides one possible approach to the analysis of multivariate data.Among other it can be also used for classification purposes. The present paper is an overview of the research in the field of depth-based classification for multivariate data.It provides a short summary of current state of knowledge in the field of depth-based classification followed by detailed discussion of four main directions in the depth-based classification, namely semiparametric depth-based classifiers, maximal depth classifier, (maximal depth) classifiers which use local depth functions and finally advanced depth-based classifiers.We do not restrict our attention only on proposed classifiers. The paper rather aims to overview the ideas connected with depth-based classification and problems that were discussed in this context.

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Ieva, Francesca, and Anna M. Paganoni. "Depth Measures for Multivariate Functional Data." Communications in Statistics - Theory and Methods 42, no. 7 (April 2013): 1265–76. http://dx.doi.org/10.1080/03610926.2012.746368.

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Cascos, Ignacio, and Ilya Molchanov. "Multivariate risks and depth-trimmed regions." Finance and Stochastics 11, no. 3 (May 15, 2007): 373–97. http://dx.doi.org/10.1007/s00780-007-0043-7.

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Tat, Samaneh, and Mohammad Reza Faridrohani. "Predicting depth value of the future depth-based multivariate record." Communications for Statistical Applications and Methods 30, no. 5 (September 30, 2023): 453–65. http://dx.doi.org/10.29220/csam.2023.30.5.453.

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Muthukrishnan, R., and Surabhi S. Nair. "Computing Robust Measure of Location on Multivariate Statistical Data Using Euclidean Depth Procedures." Indian Journal Of Science And Technology 16, no. 26 (July 23, 2023): 1927–34. http://dx.doi.org/10.17485/ijst/v16i26.847.

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He, Xuming, and Gang Wang. "Convergence of depth contours for multivariate datasets." Annals of Statistics 25, no. 2 (April 1997): 495–504. http://dx.doi.org/10.1214/aos/1031833661.

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Tsao, Min. "An empirical depth function for multivariate data." Statistics & Probability Letters 83, no. 1 (January 2013): 213–18. http://dx.doi.org/10.1016/j.spl.2012.09.007.

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10

Romanazzi, Mario. "Data depth, random simplices and multivariate dispersion." Statistics & Probability Letters 79, no. 12 (June 2009): 1473–79. http://dx.doi.org/10.1016/j.spl.2009.03.022.

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López-Pintado, Sara, Ying Sun, Juan K. Lin, and Marc G. Genton. "Simplicial band depth for multivariate functional data." Advances in Data Analysis and Classification 8, no. 3 (March 5, 2014): 321–38. http://dx.doi.org/10.1007/s11634-014-0166-6.

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12

Velasco-Forero, S., and J. Angulo. "Random Projection Depth for Multivariate Mathematical Morphology." IEEE Journal of Selected Topics in Signal Processing 6, no. 7 (November 2012): 753–63. http://dx.doi.org/10.1109/jstsp.2012.2211336.

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13

Quek, Yihui, Eneet Kaur, and Mark M. Wilde. "Multivariate trace estimation in constant quantum depth." Quantum 8 (January 10, 2024): 1220. http://dx.doi.org/10.22331/q-2024-01-10-1220.

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There is a folkloric belief that a depth-Θ(m) quantum circuit is needed to estimate the trace of the product of m density matrices (i.e., a multivariate trace), a subroutine crucial to applications in condensed matter and quantum information science. We prove that this belief is overly conservative by constructing a constant quantum-depth circuit for the task, inspired by the method of Shor error correction. Furthermore, our circuit demands only local gates in a two dimensional circuit – we show how to implement it in a highly parallelized way on an architecture similar to that of Google's Sycamore processor. With these features, our algorithm brings the central task of multivariate trace estimation closer to the capabilities of near-term quantum processors. We instantiate the latter application with a theorem on estimating nonlinear functions of quantum states with "well-behaved" polynomial approximations.

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Chebana, Fateh, and Taha B. M. J. Ouarda. "Multivariate extreme value identification using depth functions." Environmetrics 22, no. 3 (March 24, 2011): 441–55. http://dx.doi.org/10.1002/env.1089.

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15

Li, Jun, and Regina Y. Liu. "Multivariate spacings based on data depth: I. Construction of nonparametric multivariate tolerance regions." Annals of Statistics 36, no. 3 (June 2008): 1299–323. http://dx.doi.org/10.1214/07-aos505.

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Hubert, Mia, Peter Rousseeuw, and Pieter Segaert. "Multivariate and functional classification using depth and distance." Advances in Data Analysis and Classification 11, no. 3 (August 17, 2016): 445–66. http://dx.doi.org/10.1007/s11634-016-0269-3.

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17

Liu, Zhenyu, Reza Modarres, and Mengta Yang. "A multivariate control quantile test using data depth." Computational Statistics & Data Analysis 57, no. 1 (January 2013): 262–70. http://dx.doi.org/10.1016/j.csda.2012.06.013.

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18

Massé, Jean-Claude. "Multivariate trimmed means based on the Tukey depth." Journal of Statistical Planning and Inference 139, no. 2 (February 2009): 366–84. http://dx.doi.org/10.1016/j.jspi.2008.03.038.

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19

Vardi, Y., and C. H. Zhang. "The multivariate L1-median and associated data depth." Proceedings of the National Academy of Sciences 97, no. 4 (February 15, 2000): 1423–26. http://dx.doi.org/10.1073/pnas.97.4.1423.

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20

Bayat, Sara, and Sakineh Dehghan. "Multi-class Depth-based Classification for Multivariate Data." Journal of Statistical Sciences 17, no. 2 (February 1, 2024): 0. http://dx.doi.org/10.61186/jss.17.2.5.

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21

Medina, Cecilia, Jesús H. Camacho-Tamayo, and César A. Cortés. "Soil penetration resistance analysis by multivariate and geostatistical methods." Engenharia Agrícola 32, no. 1 (February 2012): 91–101. http://dx.doi.org/10.1590/s0100-69162012000100010.

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The penetration resistance (PR) is a soil attribute that allows identifies areas with restrictions due to compaction, which results in mechanical impedance for root growth and reduced crop yield. The aim of this study was to characterize the PR of an agricultural soil by geostatistical and multivariate analysis. Sampling was done randomly in 90 points up to 0.60 m depth. It was determined spatial distribution models of PR, and defined areas with mechanical impedance for roots growth. The PR showed a random distribution to 0.55 and 0.60 m depth. PR in other depths analyzed showed spatial dependence, with adjustments to exponential and spherical models. The cluster analysis that considered sampling points allowed establishing areas with compaction problem identified in the maps by kriging interpolation. The analysis with main components identified three soil layers, where the middle layer showed the highest values of PR.

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22

Serfling, Robert. "Generalized Quantile Processes Based on Multivariate Depth Functions, with Applications in Nonparametric Multivariate Analysis." Journal of Multivariate Analysis 83, no. 1 (October 2002): 232–47. http://dx.doi.org/10.1006/jmva.2001.2044.

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23

Mirzargar, Mahsa, and Jeffrey L. Anderson. "On Evaluation of Ensemble Forecast Calibration Using the Concept of Data Depth." Monthly Weather Review 145, no. 5 (April 10, 2017): 1679–90. http://dx.doi.org/10.1175/mwr-d-16-0351.1.

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Abstract Various generalizations of the univariate rank histogram have been proposed to inspect the reliability of an ensemble forecast or analysis in multidimensional spaces. Multivariate rank histograms provide insightful information about the misspecification of genuinely multivariate features such as the correlation between various variables in a multivariate ensemble. However, the interpretation of patterns in a multivariate rank histogram should be handled with care. The purpose of this paper is to focus on multivariate rank histograms designed based on the concept of data depth and outline some important considerations that should be accounted for when using such multivariate rank histograms. To generate correct multivariate rank histograms using the concept of data depth, the datatype of the ensemble should be taken into account to define a proper preranking function. This paper demonstrates how and why some preranking functions might not be suitable for multivariate or vector-valued ensembles and proposes preranking functions based on the concept of simplicial depth that are applicable to both multivariate points and vector-valued ensembles. In addition, there exists an inherent identifiability issue associated with center-outward preranking functions used to generate multivariate rank histograms. This problem can be alleviated by complementing the multivariate rank histogram with other well-known multivariate statistical inference tools based on rank statistics such as the depth-versus-depth (DD) plot. Using a synthetic example, it is shown that the DD plot is less sensitive to sample size compared to multivariate rank histograms.

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24

González-De La Fuente, Luis González-De La, Alicia Nieto-Reyes, and Pedro Terán. "Properties of Statistical Depth with Respect to Compact Convex Random Sets: The Tukey Depth." Mathematics 10, no. 15 (August 3, 2022): 2758. http://dx.doi.org/10.3390/math10152758.

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We study a statistical data depth with respect to compact convex random sets, which is consistent with the multivariate Tukey depth and the Tukey depth for fuzzy sets. In addition, it provides a different perspective to the existing halfspace depth with respect to compact convex random sets. In studying this depth function, we provide a series of properties for the statistical data depth with respect to compact convex random sets. These properties are an adaptation of properties that constitute the axiomatic notions of multivariate, functional, and fuzzy depth-functions and other well-known properties of depth.

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Tat, Samaneh, and Mohammad Reza Faridrohani. "A new type of multivariate records: depth-based records." Statistics 55, no. 2 (March 4, 2021): 296–320. http://dx.doi.org/10.1080/02331888.2021.1925280.

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26

Dehghan, Sakineh, and Mohamadreza Faridrohani. "Multivariate Outlier Detection Based on Depth-Based Outlyingness Function." Journal of Statistical Sciences 15, no. 2 (March 1, 2022): 443–62. http://dx.doi.org/10.52547/jss.15.2.443.

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27

Dovoedo, Y. H., and S. Chakraborti. "Power of depth-based nonparametric tests for multivariate locations." Journal of Statistical Computation and Simulation 85, no. 10 (May 6, 2014): 1987–2006. http://dx.doi.org/10.1080/00949655.2014.913045.

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28

Pawar, Somanath D., and Digambar T. Shirke. "Nonparametric tests for multivariate locations based on data depth." Communications in Statistics - Simulation and Computation 48, no. 3 (December 6, 2017): 753–76. http://dx.doi.org/10.1080/03610918.2017.1397165.

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29

Chenouri, Shojaeddin, and Christopher G. Small. "A nonparametric multivariate multisample test based on data depth." Electronic Journal of Statistics 6 (2012): 760–82. http://dx.doi.org/10.1214/12-ejs692.

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30

Ciupke, Krzysztof. "Multivariate Process Capability Index Based on Data Depth Concept." Quality and Reliability Engineering International 32, no. 7 (January 10, 2016): 2443–53. http://dx.doi.org/10.1002/qre.1947.

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31

Chenouri, Shojaeddin, Ahmad Mozaffari, and Gregory Rice. "Robust multivariate change point analysis based on data depth." Canadian Journal of Statistics 48, no. 3 (March 5, 2020): 417–46. http://dx.doi.org/10.1002/cjs.11541.

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32

Shi, Xiaoping, Yue Zhang, and Yuejiao Fu. "Two-Sample Tests Based on Data Depth." Entropy 25, no. 2 (January 28, 2023): 238. http://dx.doi.org/10.3390/e25020238.

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In this paper, we focus on the homogeneity test that evaluates whether two multivariate samples come from the same distribution. This problem arises naturally in various applications, and there are many methods available in the literature. Based on data depth, several tests have been proposed for this problem but they may not be very powerful. In light of the recent development of data depth as an important measure in quality assurance, we propose two new test statistics for the multivariate two-sample homogeneity test. The proposed test statistics have the same χ2(1) asymptotic null distribution. The generalization of the proposed tests into the multivariate multisample situation is discussed as well. Simulations studies demonstrate the superior performance of the proposed tests. The test procedure is illustrated through two real data examples.

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33

Al-Guraibawi, Mohammed, and Baher Mohammed. "Regression Depth for Statistical Depth Function." Journal of Al-Rafidain University College For Sciences ( Print ISSN: 1681-6870 ,Online ISSN: 2790-2293 ), no. 1 (January 14, 2024): 539–46. http://dx.doi.org/10.55562/jrucs.v54i1.621.

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The statistical depth function is one of the modern approaches that can be used for developing multivariate robust regression based on robust estimates of the location and dispersion matrix. One merit advantage of the depth concept is that it can be used directly to provide deeper estimation functions for data location and regression parameters in a multidimensional environment. The deeper estimation functions induced by depth are expected to inherit the desired and inherent robustness properties (such as limited maximum bias, impact function, and high breaking point) as do their counterparts at univariate sites. Investigation. The main objective of this article is to check the power of the statistical depth function throw the depth regression, it turns out that the deepest functional projection possesses a finite effect function and the best possible asymptotic breakpoint as well as the best breaking point of a finite sample compared with some classical and robust existed method.

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34

Lian, Bin, Chuanliang Cui, Li Zhou, Xin Song, Xiaoshi Zhang, Di Wu, Zhihong Chi, et al. "Multivariate analysis of prognostic factors among 706 mucosal melanoma patients." Journal of Clinical Oncology 35, no. 15_suppl (May 20, 2017): 9569. http://dx.doi.org/10.1200/jco.2017.35.15_suppl.9569.

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9569 Background: Mucosal melanoma is rare and associated with extremely poor prognosis. Little is known about its outcome and prognostic analysis. In this study, we evaluated prognostic factors among mucosal melanomas. Methods: The survival rates, Relapse Free Survival (RFS), Overall Survival (OS) and prognostic factors were compared for 706 mucosal melanomas at different anatomical sites. Results: Mucosal melanoma from nasal pharyngeal and oral (268 pts), upper and lower gastrointestinal (GI) (221 pts), gynecological and urological (196 pts) had a similar survival with a 1-y survival rate (88%, 83%, 86%), 2-y survival rate (66%, 57%, 61%), 5-y survival rate (27%, 16%, 20%), respectively. Multivariate analysis revealed that Depth of Invasion (p < 0.001), Lymph node metastases (p < 0.001), Distant metastases (p < 0.001) were three independent prognostic factors for OS among 706 pts. Anatomical site (p = 0.031), Depth of Invasion (p < 0.001), Lymph node metastases (p < 0.001) were three independent prognostic factors for RFS among 543 pts. KPS status, Depth of Invasion, Lymph node metastases, Distant metastases were independent factors for OS among nasal pharyngeal and oral pts. Depth of Invasion, Lymph node metastases, CKIT Mutation were independent factors for RFS among nasal pharyngeal and oral pts. Gender, Lymph node metastases, Distant metastases were independent factors for OS among GI pts. Gender, Depth of Invasion, Lymph node metastases were independent factors for RFS among GI pts. Lymph node metastases, Distant metastases were independent factors for OS among Gynecological and Urological pts. Depth of Invasion, Lymph node metastases were independent factors for RFS among Gynecological and Urological pts. Conclusions: This is the first prognostic analysis for mucosal melanoma with the largest sample size for the first time. with few exceptions, It revealed that Depth of Invasion, Lymph node metastases, Distant metastases were independent prognostic factors for OS, Depth of Invasion and Lymph node metastases were independent prognostic factors for RFS. These results should be incorporated into the establishment of stage system and design of future clinical trials involving patients with mucosal melanoma.

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35

Pandolfo, Giuseppe, Carmela Iorio, Michele Staiano, Massimo Aria, and Roberta Siciliano. "Multivariate process control charts based on the L p depth." Applied Stochastic Models in Business and Industry 37, no. 2 (March 2021): 229–50. http://dx.doi.org/10.1002/asmb.2616.

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36

Dehghan, Sakineh, and Mohammad Reza Faridrohani. "Non‐parametric depth‐based tests for the multivariate location problem." Australian & New Zealand Journal of Statistics 63, no. 2 (June 2021): 309–30. http://dx.doi.org/10.1111/anzs.12328.

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37

Dang, Xin, and Robert Serfling. "Nonparametric depth-based multivariate outlier identifiers, and masking robustness properties." Journal of Statistical Planning and Inference 140, no. 1 (January 2010): 198–213. http://dx.doi.org/10.1016/j.jspi.2009.07.004.

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38

Shirke, Digambar Tukaram, and Atul Rajaram Chavan. "Multivariate multi-sample tests for location based on data depth." Journal of Statistical Computation and Simulation 89, no. 18 (September 24, 2019): 3377–90. http://dx.doi.org/10.1080/00949655.2019.1667359.

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39

Zhang, Caiya, Yanbiao Xiang, and Xinmei Shen. "Some multivariate goodness-of-fit tests based on data depth." Journal of Applied Statistics 39, no. 2 (February 2012): 385–97. http://dx.doi.org/10.1080/02664763.2011.594033.

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40

Dutta, Subhajit, and Marc G. Genton. "Depth-weighted robust multivariate regression with application to sparse data." Canadian Journal of Statistics 45, no. 2 (April 5, 2017): 164–84. http://dx.doi.org/10.1002/cjs.11315.

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41

Sena, Any, Josiclêda Domiciano Galvíncio, Valeria Costa, Rodrigo Miranda, Maria do Socorro Araujo, and Magna Soelma. "Multivariate analysis of soil moisture data." Journal of Hyperspectral Remote Sensing 7, no. 7 (May 17, 2018): 432. http://dx.doi.org/10.29150/jhrs.v7.7.p432-438.

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Soil water content is an important variable in the understanding of hydrology in agricultural and environmental systems in a region. It is known that soil moisture is related to soil characteristics, porosity, depth, hydraulic conductivity, among others, that is, characteristics that define its typology. Studies related to soil moisture are still very precarious in Brazil. Recently, the Europe Space Agency has provided soil moisture data estimated worldwide with satellite data. This availability made possible the spatial and temporal assessment of soil magna.moura@embrapa.br moisture for different studies in the world, even though we did not know the accuracy of these data. Many studies have used multivariate analysis to find groups that have similar characteristics that can be analyzed and managed with the same actions. Therefore, this study sought to analyze the similarities and dissimilarities between soil types when considering the characteristics of soil moisture, precipitation, soil elevation and soil depth. After applying the statistical methods it was possible to perceive that the soil moisture does not depend strongly on the precipitation and to suggest caution in the analysis of the relations between the humidity factor and the others scored.

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42

Frontalini, Fabrizio, Michael A. Kaminski, Rodolfo Coccioni, and Michal Kowalewski. "Agglutinated vs. calcareous foraminiferal assemblages as bathymetric proxies: Direct multivariate tests from modern environments." Micropaleontology 64, no. 6 (2018): 403–15. http://dx.doi.org/10.47894/mpal.64.6.06.

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Benthic foraminiferal assemblages, used widely as paleoenvironmental indicators, can potentially provide numerical estimates of relative water depth. The quality of this bathymetric proxy was tested here directly using onshore-offshore transects across two present-day marine basins: (1) Saros Bay (northern Aegean Sea), with sampling sites ranging from 15 to 500 m water depth; and (2) Marmara Sea (between Black Sea and Aegean Sea), with sampling sites ranging from 15 to 350 m water depth. For both marine basins, multivariate ordinations of calcareous and agglutinated foraminifera demonstrated that samples varied predictably in faunal composition along regional depth gradients. The multivariate ordination scores and water depthwere highly and positively correlated in all cases: r2 = 0.74 (Saros Bay, agglutinated foraminifera), r2 = 0.67 (Saros Bay, calcareous foraminifera), r2 = 0.68 (Marmara Sea, agglutinated foraminifera), and r2 = 0.96 (Marmara Sea, calcareous foraminifera). Comparably robust relationships between ordination scores and water depth were observed when data were pooled across basins and/or foraminiferal type. These results suggest that both agglutinated and calcareous benthic foraminifera provide robust quantitative proxies of water depth. Multivariate ordinations based on agglutinated foraminiferamay potentially yield numerical estimates of water depth in the geological record and provide a quantitative environmental framework for paleontological and stratigraphic interpretations.

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43

Belcher, J. W., P. A. Keddy, and P. M. Catling. "Alvar vegetation in Canada: a multivariate description at two scales." Canadian Journal of Botany 70, no. 6 (June 1, 1992): 1279–91. http://dx.doi.org/10.1139/b92-161.

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Alvars are areas with a distinctive dry grassland vegetation growing in thin soil over level limestone, and they are documented in Scandinavia, the eastern United States, and central Canada. Ordination and classification analysis techniques were used to describe alvar vegetation in Canada at two scales: within one alvar and among four alvar sites. Within one alvar, changes in species composition corresponded to changes in soil depth and biomass. There were two main vegetation types: (i) alvar meadows with complete vegetation cover and (ii) rock flats with incomplete vegetation cover over limestone rock. Among alvars, species composition was related primarily to geographic location. The southern site was distinct from the eastern and northern sites. Relationships between soil depth, plant biomass, and vegetation could also be detected. At within and among alvar scales, tall perennial graminoids dominated sites with deep soil while small annuals and stress-tolerant perennials dominated shallow soil sites. Average biomass levels were strongly positively correlated with soil depth across vegetation types. Average species richness was curvilinearly related to biomass. Our results describe Canadian alvar vegetation and illustrate important differences among alvar sites, showing that a number of these sites need protection to conserve alvar vegetation. Key words: grassland, drought, soil depth, species richness, biomass, conservation.

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44

Zhou, Xinyu, and Wei Wu. "Statistical Depth in Spatial Point Process." Mathematics 12, no. 4 (February 17, 2024): 595. http://dx.doi.org/10.3390/math12040595.

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Statistical depth is widely used as a powerful tool to measure the center-outward rank of multivariate and functional data. Recent studies have introduced the notion of depth to the temporal point process, which exhibits randomness in the cardinality as well as distribution in the observed events. The proposed methods can well capture the rank of a point process in a given time interval, where a critical step is to measure the rank by using inter-arrival events. In this paper, we propose to extend the depth concept to multivariate spatial point process. In this case, the observed process is in a multi-dimensional location and there are no conventional inter-arrival events in the temporal process. We adopt the newly developed depth in metric space by defining two different metrics, namely the penalized metric and the smoothing metric, to fully explore the depth in the spatial point process. The mathematical properties and the large sample theory, as well as depth-based hypothesis testings, are thoroughly discussed. We then use several simulations to illustrate the effectiveness of the proposed depth method. Finally, we apply the new method in a real-world dataset and obtain desirable ranking performance.

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45

Liu, Regina Y., and Kesar Singh. "A Quality Index Based on Data Depth and Multivariate Rank Tests." Journal of the American Statistical Association 88, no. 421 (March 1993): 252. http://dx.doi.org/10.2307/2290720.

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46

Gao, Yonghong. "Depth Based Permutation Test For General Differences In Two Multivariate Populations." Journal of Modern Applied Statistical Methods 3, no. 1 (May 1, 2004): 49–53. http://dx.doi.org/10.22237/jmasm/1083369960.

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47

Van Ootegem, L., K. Van Herck, T. Creten, E. Verhofstadt, L. Foresti, E. Goudenhoofdt, M. Reyniers, L. Delobbe, D. Murla Tuyls, and P. Willems. "Exploring the potential of multivariate depth-damage and rainfall-damage models." Journal of Flood Risk Management 11 (January 3, 2017): S916—S929. http://dx.doi.org/10.1111/jfr3.12284.

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48

Haghiabi, Amir Hamzeh. "Prediction of River Pipeline Scour Depth Using Multivariate Adaptive Regression Splines." Journal of Pipeline Systems Engineering and Practice 8, no. 1 (February 2017): 04016015. http://dx.doi.org/10.1061/(asce)ps.1949-1204.0000248.

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49

Kuhnt, Sonja, and André Rehage. "An angle-based multivariate functional pseudo-depth for shape outlier detection." Journal of Multivariate Analysis 146 (April 2016): 325–40. http://dx.doi.org/10.1016/j.jmva.2015.10.016.

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50

Pawar, Somanath D., and Digambar T. Shirke. "Nonparametric tests for multivariate multi-sample locations based on data depth." Journal of Statistical Computation and Simulation 89, no. 9 (March 17, 2019): 1574–91. http://dx.doi.org/10.1080/00949655.2019.1590577.

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Journal articles on the topic 'Multivariate depth'

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