Correction: Pfeifer, D.; Ragulina, O. Adaptive Bernstein Copulas and Risk Management. Mathematics 2020, 8, 2221

Pfeifer, Dietmar; Ragulina, Olena

doi:10.3390/math9141646

Cited by 3 publications

(14 citation statements)

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“…, x d q P R d . (10) Please note that in the case that g is a d-dimensional cumulative distribution function of a probability measure P on the d-dimensional Borel σ-field B d , then ∆g b a " P…”

Section: Some Important Facts About Multivariate Bernstein Polynomialsmentioning

confidence: 99%

“…Please note that Proposition 3 is already implicitly formulated in [5,10] (see also [15] (Chapter 4.1.2)). We reformulate the corresponding statements there in an appropriate way.…”

Section: Some Important Facts About Multivariate Bernstein Polynomialsmentioning

confidence: 99%

“…Bernstein copulas, which can be considered to be Bernstein polynomials for empirical and other copula functions, have a long tradition in nonparametric modelling of dependence structures in arbitrary dimensions, in particular, with applications in risk management, and have come into a deeper focus in the recent years. There is an extensive list of research papers on this topic, for instance, [3][4][5][6][7][8][9][10][11][12][13][14]. In particular, the monographs [15,16] have devoted separate chapters to the topic of Bernstein copulas.…”

Section: Introductionmentioning

confidence: 99%

“…A very important aspect of Bernstein copulas lies in Monte Carlo simulation techniques of dependence structures, in particular, in higher dimensions. The structure of such procedures ranges from very complex (see, e.g., [10]) to extremely simple (see, e.g., [5]), such that Monte Carlo simulations could, for instance, be performed easily with ordinary spreadsheets, in particular, in applications concerning quantitative risk management.…”

Section: Introductionmentioning

confidence: 99%

“…In comparison with classical parametric dependence models such as elliptically contoured or Archimedean copulas, this is probably a nondesirable property. In particular, this problem has been tackled seemingly first in [10] by approximating the underlying discrete skeleton for the Bernstein copula by a least-squares approach and recently in the Ph.D. thesis [18], where cluster analytic methods were used.…”

Section: Introductionmentioning

confidence: 99%

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Adaptive Bernstein Copulas and Risk Management

Pfeifer

Ragulina

2020

Mathematics

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We present a constructive approach to Bernstein copulas with an admissible discrete skeleton in arbitrary dimensions when the underlying marginal grid sizes are smaller than the number of observations. This prevents an overfitting of the estimated dependence model and reduces the simulation effort for Bernstein copulas a lot. In a case study, we compare different approaches of Bernstein and Gaussian copulas regarding the estimation of risk measures in risk management.

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Section: Some Important Facts About Multivariate Bernstein Polynomialsmentioning

confidence: 99%

“…Please note that Proposition 3 is already implicitly formulated in [5,10] (see also [15] (Chapter 4.1.2)). We reformulate the corresponding statements there in an appropriate way.…”

Section: Some Important Facts About Multivariate Bernstein Polynomialsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Adaptive Bernstein Copulas and Risk Management

Pfeifer

Ragulina

2020

Mathematics

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A new nonparametric copula framework for the joint analysis of river temperature and low flow characteristics for aquatic habitat risk assessment

Latif

Ouarda

St‐Hilaire

et al. 2023

Preprint

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The joint probability analysis of river water temperature (RWT) and low flow (LF) characteristics is essential as their combined effect can negatively affect aquatic species, e.g., ectotherm fish. Traditional multivariate models may not be as effective as copula-based methodologies. This study introduces a new multivariate approach, the nonparametric copula density framework, free from any distribution assumption in their univariate margins and copula joint density. The proposed framework utilized RWT and LF datasets collected at five different river stations in Switzerland. The study evaluates a nonparametric Gaussian kernel with six bandwidth selectors to model marginal densities. It employs nonparametric-based Beta kernel density, Bernstein estimator, and Transformation kernel estimator to approximate copula density with nonparametric and parametric margins. The performance of some parametric copula densities was also compared. The most justifiable models were employed to estimate bivariate joint exceedance probabilities and return periods (RPs). The Beta kernel copula with Gaussian kernel margins outperformed other models for most stations; Bernstein and Transformation copula with Gaussian kernel margins were better for only one station each. The univariate RPs (RWT or LF) are lower than the AND-joint but higher than OR joint case. As the percentile value of LF events (serve as a conditioning variable) increases, the bivariate joint RPs of RWT also increase. Higher values in RWT events result in higher RPs than lower values at the fixed percentile value of LF. All such estimated risk statistics are beneficial to analyze their mutual risk in aquatic habitats and freshwater ecosystems.

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Vine Copula-Based Multivariate Distribution of Rainfall Intensity, Wind Speed, and Wind Direction for Optimizing Qatari Meteorological Stations

Qasem,

Joergensen,

Rahman

et al. 2024

Water

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This study employs copula functions to establish the dependency structure of the joint distribution among rainfall intensity, wind speed, and wind direction in Qatar. Based on a Vine Copula, the trivariate distribution between rainfall intensity, wind speed, and wind direction is found to exhibit a root-mean-square error (RMSE) of 0.0072 on the observed vs. modeled cumulative probabilities using ranked normalized observations. It is also found that the winter Shamal winds are most pronounced during rainfall. However, a secondary component of easterly winds known as the Kaus winds is also found to exert an important influence. This wind pattern is observable during rainfall at all the selected stations, albeit with minor variations. It is also found that rainfall stations where the rainfall is obstructed in any way from northwest to north and from east to southeast significantly influence the rainfall measurements. Specific rain gauges in Qatar are found to be situated in disrupted surroundings, such as meteorological stations close to passing traffic, where road spray could infiltrate the rain gauge funnel, impacting the accuracy of rainfall measurements. The study results necessitated the relocation of approximately half of these roadside gauges to mitigate wind-induced biases from road spray. An evaluation of operations is recommended for approximately 80 meteorological stations responsible for measuring rainfall in Qatar. The methodology devised in this study holds potential for application to other Middle Eastern countries and regions with similar climates.

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Correction: Pfeifer, D.; Ragulina, O. Adaptive Bernstein Copulas and Risk Management. Mathematics 2020, 8, 2221

Abstract: The authors wish to make the following corrections to this paper [1]:1 [...]

Cited by 3 publications

References 1 publication

Adaptive Bernstein Copulas and Risk Management

Adaptive Bernstein Copulas and Risk Management

A new nonparametric copula framework for the joint analysis of river temperature and low flow characteristics for aquatic habitat risk assessment

Vine Copula-Based Multivariate Distribution of Rainfall Intensity, Wind Speed, and Wind Direction for Optimizing Qatari Meteorological Stations

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