High dimensional Gaussian copula graphical model with FDR control

2017 ◽  
Vol 113 ◽  
pp. 457-474 ◽  
Author(s):  
Yong He ◽  
Xinsheng Zhang ◽  
Pingping Wang ◽  
Liwen Zhang
Keyword(s):  
Graphical Model ◽  
Gaussian Copula ◽  
High Dimensional

Joint estimation of multiple high-dimensional Gaussian copula graphical models

2017 ◽  
Vol 59 (3) ◽  
pp. 289-310 ◽  
Author(s):  
Yong He ◽  
Xinsheng Zhang ◽  
Jiadong Ji ◽  
Bin Liu
Keyword(s):  
Graphical Models ◽  
Joint Estimation ◽  
Gaussian Copula ◽  
High Dimensional

New Metrics for Validation of Data-Driven Random Process Models in Uncertainty Quantification

2015 ◽  
Vol 1 (2) ◽  
Author(s):  
Hongyi Xu ◽  
Zhen Jiang ◽  
Daniel W. Apley ◽  
Wei Chen
Keyword(s):  
Uncertainty Quantification ◽  
Random Process ◽  
Process Model ◽  
Goodness Of Fit ◽  
Experimental Tests ◽  
Process Models ◽  
Data Driven ◽  
Gaussian Copula ◽  
High Dimensional ◽  
Marginal Distributions

Data-driven random process models have become increasingly important for uncertainty quantification (UQ) in science and engineering applications, due to their merit of capturing both the marginal distributions and the correlations of high-dimensional responses. However, the choice of a random process model is neither unique nor straightforward. To quantitatively validate the accuracy of random process UQ models, new metrics are needed to measure their capability in capturing the statistical information of high-dimensional data collected from simulations or experimental tests. In this work, two goodness-of-fit (GOF) metrics, namely, a statistical moment-based metric (SMM) and an M-margin U-pooling metric (MUPM), are proposed for comparing different stochastic models, taking into account their capabilities of capturing the marginal distributions and the correlations in spatial/temporal domains. This work demonstrates the effectiveness of the two proposed metrics by comparing the accuracies of four random process models (Gaussian process (GP), Gaussian copula, Hermite polynomial chaos expansion (PCE), and Karhunen–Loeve (K–L) expansion) in multiple numerical examples and an engineering example of stochastic analysis of microstructural materials properties. In addition to the new metrics, this paper provides insights into the pros and cons of various data-driven random process models in UQ.

scholarly journals High-Dimensional Graphical Model Search with thegRapHDRPackage

2010 ◽  
Vol 37 (1) ◽  
Author(s):  
Gabriel C. G. Abreu ◽  
David Edwards ◽  
Rodrigo Labouriau
Keyword(s):  
Graphical Model ◽  
High Dimensional ◽  
Model Search

scholarly journals Large portfolio risk management and optimal portfolio allocation with dynamic elliptical copulas

2018 ◽  
Vol 6 (1) ◽  
pp. 19-46 ◽  
Author(s):  
Xisong Jin ◽  
Thorsten Lehnert
Keyword(s):  
Risk Management ◽  
Value At Risk ◽  
Degrees Of Freedom ◽  
Portfolio Allocation ◽  
Optimal Portfolio ◽  
Gaussian Copula ◽  
High Dimensional ◽  
Dependence Structure ◽  
Portfolio Risk ◽  
Portfolio Risk Management

Abstract Previous research has focused on the importance of modeling the multivariate distribution for optimal portfolio allocation and active risk management. However, existing dynamic models are not easily applied to high-dimensional problems due to the curse of dimensionality. In this paper, we extend the framework of the Dynamic Conditional Correlation/Equicorrelation and an extreme value approach into a series of Dynamic Conditional Elliptical Copulas. We investigate risk measures such as Value at Risk (VaR) and Expected Shortfall (ES) for passive portfolios and dynamic optimal portfolios using Mean-Variance and ES criteria for a sample of US stocks over a period of 10 years. Our results suggest that (1) Modeling the marginal distribution is important for dynamic high-dimensional multivariate models. (2) Neglecting the dynamic dependence in the copula causes over-aggressive risk management. (3) The DCC/DECO Gaussian copula and t-copula work very well for both VaR and ES. (4) Grouped t-copulas and t-copulas with dynamic degrees of freedom further match the fat tail. (5) Correctly modeling the dependence structure makes an improvement in portfolio optimization with respect to tail risk. (6) Models driven by multivariate t innovations with exogenously given degrees of freedom provide a flexible and applicable alternative for optimal portfolio risk management.

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