Relevant bibliographies by topics / Multivariate and hidden regular variation

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Multivariate and hidden regular variation'

Author: Grafiati
Published: 25 May 2024

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Journal articles on the topic "Multivariate and hidden regular variation"

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Heffernan, Janet, and Sidney Resnick. "Hidden regular variation and the rank transform." Advances in Applied Probability 37, no. 2 (2005): 393–414. http://dx.doi.org/10.1239/aap/1118858631.

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Random vectors in the positive orthant whose distributions possess hidden regular variation are a subclass of those whose distributions are multivariate regularly varying with asymptotic independence. The concept is an elaboration of the coefficient of tail dependence of Ledford and Tawn. We show that the rank transform that brings unequal marginals to the standard case also preserves the hidden regular variation. We discuss applications of the results to two examples, one involving flood risk and the other Internet data.
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Heffernan, Janet, and Sidney Resnick. "Hidden regular variation and the rank transform." Advances in Applied Probability 37, no. 02 (2005): 393–414. http://dx.doi.org/10.1017/s0001867800000239.

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Random vectors in the positive orthant whose distributions possess hidden regular variation are a subclass of those whose distributions are multivariate regularly varying with asymptotic independence. The concept is an elaboration of the coefficient of tail dependence of Ledford and Tawn. We show that the rank transform that brings unequal marginals to the standard case also preserves the hidden regular variation. We discuss applications of the results to two examples, one involving flood risk and the other Internet data.
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Resnick, Sidney I. "Multivariate regular variation on cones: application to extreme values, hidden regular variation and conditioned limit laws." Stochastics 80, no. 2-3 (2008): 269–98. http://dx.doi.org/10.1080/17442500701830423.

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Das, Bikramjit, Abhimanyu Mitra, and Sidney Resnick. "Living on the Multidimensional Edge: Seeking Hidden Risks Using Regular Variation." Advances in Applied Probability 45, no. 1 (2013): 139–63. http://dx.doi.org/10.1239/aap/1363354106.

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Multivariate regular variation plays a role in assessing tail risk in diverse applications such as finance, telecommunications, insurance, and environmental science. The classical theory, being based on an asymptotic model, sometimes leads to inaccurate and useless estimates of probabilities of joint tail regions. This problem can be partly ameliorated by using hidden regular variation (see Resnick (2002) and Mitra and Resnick (2011)). We offer a more flexible definition of hidden regular variation that provides improved risk estimates for a larger class of tail risk regions.
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Das, Bikramjit, Abhimanyu Mitra, and Sidney Resnick. "Living on the Multidimensional Edge: Seeking Hidden Risks Using Regular Variation." Advances in Applied Probability 45, no. 01 (2013): 139–63. http://dx.doi.org/10.1017/s0001867800006224.

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Multivariate regular variation plays a role in assessing tail risk in diverse applications such as finance, telecommunications, insurance, and environmental science. The classical theory, being based on an asymptotic model, sometimes leads to inaccurate and useless estimates of probabilities of joint tail regions. This problem can be partly ameliorated by using hidden regular variation (see Resnick (2002) and Mitra and Resnick (2011)). We offer a more flexible definition of hidden regular variation that provides improved risk estimates for a larger class of tail risk regions.
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Hua, Lei, Harry Joe, and Haijun Li. "Relations Between Hidden Regular Variation and the Tail Order of Copulas." Journal of Applied Probability 51, no. 1 (2014): 37–57. http://dx.doi.org/10.1239/jap/1395771412.

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We study the relations between the tail order of copulas and hidden regular variation (HRV) on subcones generated by order statistics. Multivariate regular variation (MRV) and HRV deal with extremal dependence of random vectors with Pareto-like univariate margins. Alternatively, if one uses a copula to model the dependence structure of a random vector then the upper exponent and tail order functions can be used to capture the extremal dependence structure. After defining upper exponent functions on a series of subcones, we establish the relation between the tail order of a copula and the tail
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Hua, Lei, Harry Joe, and Haijun Li. "Relations Between Hidden Regular Variation and the Tail Order of Copulas." Journal of Applied Probability 51, no. 01 (2014): 37–57. http://dx.doi.org/10.1017/s0021900200010068.

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We study the relations between the tail order of copulas and hidden regular variation (HRV) on subcones generated by order statistics. Multivariate regular variation (MRV) and HRV deal with extremal dependence of random vectors with Pareto-like univariate margins. Alternatively, if one uses a copula to model the dependence structure of a random vector then the upper exponent and tail order functions can be used to capture the extremal dependence structure. After defining upper exponent functions on a series of subcones, we establish the relation between the tail order of a copula and the tail
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Simpson, E. S., J. L. Wadsworth, and J. A. Tawn. "Determining the dependence structure of multivariate extremes." Biometrika 107, no. 3 (2020): 513–32. http://dx.doi.org/10.1093/biomet/asaa018.

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Summary In multivariate extreme value analysis, the nature of the extremal dependence between variables should be considered when selecting appropriate statistical models. Interest often lies in determining which subsets of variables can take their largest values simultaneously while the others are of smaller order. Our approach to this problem exploits hidden regular variation properties on a collection of nonstandard cones, and provides a new set of indices that reveal aspects of the extremal dependence structure not available through existing measures of dependence. We derive theoretical pr
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Mitra, Abhimanyu, and Sidney I. Resnick. "Hidden Regular Variation and Detection of Hidden Risks." Stochastic Models 27, no. 4 (2011): 591–614. http://dx.doi.org/10.1080/15326349.2011.614183.

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Maulik, Krishanu, and Sidney Resnick. "Characterizations and Examples of Hidden Regular Variation." Extremes 7, no. 1 (2004): 31–67. http://dx.doi.org/10.1007/s10687-004-4728-4.

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Dissertations / Theses on the topic "Multivariate and hidden regular variation"

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Legrand, Juliette. "Simulation and assessment of multivariate extreme models for environmental data." Electronic Thesis or Diss., université Paris-Saclay, 2022. http://www.theses.fr/2022UPASJ015.

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L'estimation précise des probabilités d'occurrence des événements extrêmes environnementaux est une préoccupation majeure dans l'évaluation des risques. Pour l'ingénierie côtière par exemple, le dimensionnement de structures implantées sur ou à proximité des côtes doit être tel qu'elles résistent aux événements les plus sévères qu'elles puissent rencontrer au cours de leur vie. Cette thèse porte sur la simulation d'événements extrêmes multivariés, motivée par des applications aux hauteurs significatives de vagues, et sur l'évaluation de modèles de prédiction d'occurrence d'événements extrêmes.
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Mariko, Dioulde Habibatou. "Multivariate Regular Variation and its Applications." Thesis, Université d'Ottawa / University of Ottawa, 2015. http://hdl.handle.net/10393/32756.

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In this thesis, we review the basic notions related to univariate regular variation and study some fundamental properties of regularly varying random variables. We then consider the notion of regular variation in the multivariate case. After collecting some results from multivariate regular variation for random vectors with values in $\mathbb{R}_{+}^{d}$, we discuss its properties and examine several examples of multivariate regularly varying random vectors such as independent and identically distributed random vectors, fully dependent random vectors and other models. We also present the elem
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Tong, Zhigang. "Statistical Inference for Heavy Tailed Time Series and Vectors." Thesis, Université d'Ottawa / University of Ottawa, 2017. http://hdl.handle.net/10393/35649.

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In this thesis we deal with statistical inference related to extreme value phenomena. Specifically, if X is a random vector with values in d-dimensional space, our goal is to estimate moments of ψ(X) for a suitably chosen function ψ when the magnitude of X is big. We employ the powerful tool of regular variation for random variables, random vectors and time series to formally define the limiting quantities of interests and construct the estimators. We focus on three statistical estimation problems: (i) multivariate tail estimation for regularly varying random vectors, (ii) extremogram e
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Yuan, Zhongyi. "Quantitative analysis of extreme risks in insurance and finance." Diss., University of Iowa, 2013. https://ir.uiowa.edu/etd/2422.

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In this thesis, we aim at a quantitative understanding of extreme risks. We use heavy-tailed distribution functions to model extreme risks, and use various tools, such as copulas and MRV, to model dependence structures. We focus on modeling as well as quantitatively estimating certain measurements of extreme risks. We start with a credit risk management problem. More specifically, we consider a credit portfolio of multiple obligors subject to possible default. We propose a new structural model for the loss given default, which takes i
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Hitz, Adrien. "Modelling of extremes." Thesis, University of Oxford, 2016. https://ora.ox.ac.uk/objects/uuid:ad32f298-b140-4aae-b50e-931259714085.

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This work focuses on statistical methods to understand how frequently rare events occur and what the magnitude of extreme values such as large losses is. It lies in a field called extreme value analysis whose scope is to provide support for scientific decision making when extreme observations are of particular importance such as in environmental applications, insurance and finance. In the univariate case, I propose new techniques to model tails of discrete distributions and illustrate them in an application on word frequency and multiple birth data. Suitably rescaled, the limiting tails of som
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Eder, Irmingard [Verfasser]. "First passage events and multivariate regular variation for dependent Lévy processes with applications in insurance / Irmingard Marianne Margarethe Eder." 2009. http://d-nb.info/996373233/34.

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Janßen, Anja. "Über Zusammenhänge von leichten Tails, regulärer Variation und Extremwerttheorie." Doctoral thesis, 2010. http://hdl.handle.net/11858/00-1735-0000-0006-B69F-1.

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Books on the topic "Multivariate and hidden regular variation"

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Omey, E. Multivariate regular variation and applications in probability theory. Economische Hogeschool Sint-Aloysius, 1989.

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Book chapters on the topic "Multivariate and hidden regular variation"

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Resnick, Sidney I. "Multivariate Extremes." In Extreme Values, Regular Variation and Point Processes. Springer New York, 1987. http://dx.doi.org/10.1007/978-0-387-75953-1_6.

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Li, Haijun. "Toward a Copula Theory for Multivariate Regular Variation." In Copulae in Mathematical and Quantitative Finance. Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-35407-6_9.

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"Multivariate Regular Variation." In Inference for Heavy-Tailed Data Analysis. Elsevier, 2017. http://dx.doi.org/10.1016/b978-0-12-804676-0.00004-3.

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"Multivariate regular variation." In Risk Theory. WORLD SCIENTIFIC, 2017. http://dx.doi.org/10.1142/9789813223158_0013.

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Rangeti, Innocent, and Bloodless Dzwairo. "Interpretation of Water Quality Data in uMngeni Basin (South Africa) Using Multivariate Techniques." In River Basin Management - Sustainability Issues and Planning Strategies. IntechOpen, 2021. http://dx.doi.org/10.5772/intechopen.94845.

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The major challenge with regular water quality monitoring programmes is making sense of the large and complex physico-chemical data-sets that are generated in a comparatively short period of time. Consequentially, this presents difficulties for water management practitioners who are expected to make informed decisions based on information extracted from the large data-sets. In addition, the nonlinear nature of water quality data-sets often makes it difficult to interpret the spatio-temporal variations. These reasons necessitated the need for effective methods of interpreting water quality results and drawing meaningful conclusions. Hence, this study applied multivariate techniques, namely Cluster Analysis and Principal Component Analysis, to interpret eight-year (2005–2012) water quality data that was generated from a monitoring exercise at six stations in uMngeni Basin, South Africa. The principal components extracted with eigenvalues of greater than 1 were interpreted while considering the pollution issues in the basin. These extracted components explain 67–76% of the water quality variation among the stations. The derived significant parameters suggest that uMngeni Basin was mainly affected by the catchment’s geological processes, surface runoff, domestic sewage effluent, seasonal variation and agricultural waste. Cluster Analysis grouped the sampling six stations into two clusters namely heavy (B) or low (A), based on the degree of pollution. Cluster A mainly consists of water sampling stations that were located in the outflow of the dam (NDO, IDO, MDO and NDI) and its water can be described as of fairly good quality due to dam retention and attenuation effects. Cluster B mainly consist of dam inflow water sampling stations (MDI and IDI), which can be described as polluted if compared to cluster A. The poor quality water observed at Cluster B sampling stations could be attributed to natural and anthropogenic activities through point source and runoff. The findings could assist in determining an appropriate set of water quality parameters that would indicate variation of water quality in the basin, with minimum loss of information. It is, therefore, recommended that this approach be used to assist decision-makers regarding strategies for minimising catchment pollution.
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Conference papers on the topic "Multivariate and hidden regular variation"

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OLUWAJIRE, OLUWATIMILEHIN, KATHERINE BERKOWITZ, and LANDON GRACE. "A PERFORMANCE COMPARISON OF LOW-COST NIR NANO TO NIR MICROPHAZIR FOR POLYMER COMPOSITE CHARACTERIZATION." In Proceedings for the American Society for Composites-Thirty Eighth Technical Conference. Destech Publications, Inc., 2023. http://dx.doi.org/10.12783/asc38/36559.

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Polymer composites are increasingly adopted to complement or replace their metal counterparts used in aerospace, wind turbine, automotive, and other safety-critical structures. However, these structures are susceptible to the development of undetected sub-surface damage, such as low velocity impact damage (LVI), that limits their performance and utility in certain cases. The ability to detect and monitor the progression of this type of damage from the micron level prior to growth to the macroscale is critical to ensuring the long-term safety and reliability of these structures. Near Infrared S
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