Multivariate Skew Normal Copula for Asymmetric Dependence: Estimation and Application

Wei, Zheng; Kim, Seong-Yong; Choi, Boseung; Kim, Dae-Young

doi:10.1142/s021962201750047x

Cited by 12 publications

(7 citation statements)

References 43 publications

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“…Since the copula functions have flexibility to reflect the non-linear relationships between variables, so constructing an asymmetric distribution from nonlinear dependent variable would be of interest. Moreover, the approach of this work can be extended for modeling high-dimensional asymmetric dependence patterns, see, e.g., Wei, Kim, Choi, and Kim (2019); Kurowicka and Cooke (2006). Finally, it is well known that the asymetric distributions are frequently used as an approach to model the behavior of order statistics, see e.g., Loperfido (2008) and Sheikhi and Tata (2013).…”

Section: Discussionmentioning

confidence: 99%

Multivariate Asymmetric Distributions of Copula Related Random Variables

Sheikhi,

Arad,

Mesiar

2023

AJS

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It is known that normal distribution plays an important role in analysing symmetric data. However, this symmetric assumption may not hold in many real word and in such cases, asymmetric distribution, including skew normal distribution, are known as the best alternative. Constructing asymmetric distributions is carried out using the conditional/selection approach of several independent variable conditioning on other set of variables and this approach does not work well when the independence between variablesviolated. In this work we construct an asymmetric distribution when variables are dependent using a copula. Specifically, we consider the random vectors X and Y are connected using a copula function CX,Y and we study the selection distribution Z = (X|Y ∈ T ).We present some special cases of our proposed distribution, among them, multivariate skew-normal distribution. Some properties such as moments and moment generating function are investigated. Also, numerical analysis including simulation study as well asa real data set analysis are presented for illustration.

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Section: Discussionmentioning

confidence: 99%

Multivariate Asymmetric Distributions of Copula Related Random Variables

Sheikhi,

Arad,

Mesiar

2023

AJS

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“…Wu et al (2014) uses a nonparametric Bayesian approach to construct infinite mixture skew normal copula. Wei et al (2019) explored some theoretical properties of the skew normal copula. Alternatively, Archimedean families of copulas are another solution for the issue.…”

Section: Elliptical Copulasmentioning

confidence: 99%

Bayesian mixture copula estimation and selection

Liu

Xie

2022

Preprint

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Mixture copula is a popular and essential tool for studying complex dependencies among variables. However, selecting the correct mixture models often involve repeated testing and estimations, which could cause effort and time. In this paper, we propose a method that would enable us to select and estimate the correct mixture copula simultaneously. This is done by first overfitting the model, then conducting the Bayesian estimation. We verify the correctness of our approach by numerical simulation. Finally, the real data analysis is done by studying the dependencies among three major financial markets. MSC 2020: 6208, 62F15, 62H05, 62H30

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“…Instead, we may extract Kendall's tau coefficient from the copula functions to compare correlations. Kendall's tau coefficient is measured by the difference between the probability of concordance and the probability of discordance of two pairs of random variables [42]. The Kendall's tau (τ) for the random vector (X, Y) T is defined as…”

Section: Copula Functionsmentioning

confidence: 99%

A Simultaneous Stochastic Frontier Model with Dependent Error Components and Dependent Composite Errors: An Application to Chinese Banking Industry

Liu

Rahman

et al. 2020

Mathematics

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The paper develops a simultaneous equations stochastic frontier model (SFM) with dependent random noise and inefficiency components of individual equations as well as allowing dependence across all equations of the model using copula functions. First, feasibility of our developed model was verified via two simulation studies. Then the model was applied to assess cost efficiency and market power of the banking industry of China using a panel data of 37 banks covering the period 2013–2018. Results confirmed that our simultaneous SFM with dependent random noise and inefficiency components outperformed its predecessor, which is a simultaneous SFM with dependent composite errors but with independent random noise and inefficiency components of individual SFMs as well as the conventional single-equation SFM. Apart from the statistical and computational superiority of our developed model, we also see that Chinese banks in general have a high level of cost efficiency and that competition in the banking industry of China mainly exists in state-owned banks and joint stock banks. Presence of economies of scales as well as diseconomies of scales were found in different banks. Also, the state-owned banks embraced most sophisticated technologies thereby allowing them to operate with the highest level of cost efficiency.

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Multivariate Skew Normal Copula for Asymmetric Dependence: Estimation and Application

Cited by 12 publications

References 43 publications

Multivariate Asymmetric Distributions of Copula Related Random Variables

Multivariate Asymmetric Distributions of Copula Related Random Variables

Bayesian mixture copula estimation and selection

A Simultaneous Stochastic Frontier Model with Dependent Error Components and Dependent Composite Errors: An Application to Chinese Banking Industry

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