Estimation of the tail exponent of multivariate regular variation

Kim, Moosup; Lee, Sangyeol

doi:10.1007/s10463-016-0574-9

Cited by 6 publications

(3 citation statements)

References 14 publications

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“…For bivariate and trivariate elliptical hyperbolic and t distributions and sample size n = 1000 we report the bias and RMSE as a function of k for H k,n , γls k = γk (0) and γridge k = γk (τ k ), with τk a data-driven choice of the ridge parameter as proposed in Buitendag et al (2019). These results compare favourably with the simulation results in Figure 1 in Kim and Lee (2017). Note also that the computational effort when computing the Y values is less demanding in comparison with the volume computations in the preceding section.…”

Section: Analysis Of Multivariate Regularly Varying Distributionssupporting

confidence: 54%

“…de Valk and Segers (2019) provide general results concerning the tail limits of optimal transports for regularly varying probability measures. Whereas the estimation of γ > 0 in the univariate case has known an explosion of references starting with Hill (1975), the estimation of the EVI in the multivariate case has recently taken off with Dematteo and Clémençon (2016) and Kim and Lee (2017). Here we provide an alternative approach based on the constructed transports.…”

Section: Analysis Of Multivariate Regularly Varying Distributionsmentioning

confidence: 99%

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Center-outward quantiles and the measurement of multivariate risk

Beirlant¹,

Buitendag²,

Eustasio³

et al. 2019

Preprint

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All multivariate extensions of the univariate theory of risk measurement run into the same fundamental problem of the absence, in dimension d > 1, of a canonical ordering of R d . Based on measure transportation ideas, several attempts have been made recently in the statistical literature to overcome that conceptual difficulty. In Hallin (2017), the concepts of center-outward distribution and quantile functions are developed as generalisations of the classical univariate concepts of distribution and quantile functions, along with their empirical versions. The center-outward distribution function F ± is a homeomorphic cyclically monotone mapping from± is a cyclically monotone mapping from the sample to a regular grid over B d . In dimension d = 1, F ± reduces to 2F − 1, while F (n) ± generates the same sigma-field as traditional univariate ranks. The empirical F (n) ± , however, involves a large number of ties, which is impractical in the context of risk measurement. We therefore propose a class of smooth approximations F n,ξ (ξ a smoothness index) of F (n) ± as an alternative to the interpolation developed in del Barrio et al. (2018). This approximation allows for the computation of some new empirical risk measures, based either on the convex potential associated with the proposed transports, or on the volumes of the resulting empirical quantile regions. We also discuss the role of such transports in the evaluation of the risk associated with multivariate regularly varying distributions. Some simulations and applications to case studies illustrate the value of the approach.

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Section: Analysis Of Multivariate Regularly Varying Distributionssupporting

confidence: 54%

Section: Analysis Of Multivariate Regularly Varying Distributionsmentioning

confidence: 99%

Center-outward quantiles and the measurement of multivariate risk

Beirlant¹,

Buitendag²,

Eustasio³

et al. 2019

Preprint

View full text Add to dashboard Cite

show abstract

“…Note that, in contrast to the above, the standard approach in multivariate extreme value theory is to assess the extreme behaviour component-wise for the observed multivariate signal itself (De Haan and Ferreira, 2007). Approaches which in some way acknowledge the multivariate structure of the data have been proposed only recently, and they include considering convex combinations of the component-wise estimators (Dematteo and Clémençon, 2016;Kim and Lee, 2017), extreme risk region estimation (Cai et al, 2011), and estimating the extreme value index of the generating variate of an underlying elliptical model (Dominicy et al, 2017;Heikkilä et al, 2019). However, these methods either involve complicated estimation or require strict distributional assumptions, making them less than ideal in practice.…”

Section: Introductionmentioning

confidence: 99%

Latent Model Extreme Value Index Estimation

Virta,

Lietzén,

Viitasaari

et al. 2020

Preprint

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We propose a novel strategy for multivariate extreme value index estimation. In applications such as finance, volatility and risk present in the components of a multivariate time series are often driven by the same underlying factors, such as the subprime crisis in the US. To estimate the latent risk, we apply a two-stage procedure. First, a set of * Joni Virta gratefully acknowledges the financial support from the Academy of Finland (Grant 321883). Niko Lietzén gratefully acknowledges the financial support from the Emil Aaltonen Foundation (Grant 190135 N).

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Multivariate Regular Variation

Bernardo¹

2017

Inference for Heavy-Tailed Data Analysis

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Estimation of the tail exponent of multivariate regular variation

Cited by 6 publications

References 14 publications

Center-outward quantiles and the measurement of multivariate risk

Center-outward quantiles and the measurement of multivariate risk

Latent Model Extreme Value Index Estimation

Multivariate Regular Variation

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