GHICA - Risk Analysis with GH Distributions and Independent Components

Over recent years, study on risk management has been prompted by the Basel committee for regular banking supervisory. There are however limitations of some widely-used risk management methods that either calculate risk measures under the Gaussian distributional assumption or involve numerical difficulty. The primary aim of this paper is to present a realistic and fast method, GHICA, which overcomes the limitations in multivariate risk analysis. The idea is to first retrieve independent components (ICs) out of the observed high-dimensional time series and then individually and adaptively fit the resulting ICs in the generalized hyperbolic (GH) distributional framework. For the volatility estimation of each IC, the local exponential smoothing technique is used to achieve the best possible accuracy of estimation. Finally, the fast Fourier transformation technique is used to approximate the density of the portfolio returns. The proposed GHICA method is applicable to covariance estimation as well. It is compared with the dynamic conditional correlation (DCC) method based on the simulated data with d = 50 GH distributed components. We further implement the GHICA method to calculate risk measures given 20-dimensional German DAX portfolios and a dynamic exchange rate portfolio. Several alternative methods are considered as well to compare the accuracy of calculation with the GHICA one.Multivariate Risk Management, Independent Component Analysis, Generalized Hyperbolic Distribution, Local Exponential Estimation, Value at Risk, Expected Shortfall.

Blind image separation based on exponentiated transmuted Weibull distribution

In recent years the processing of blind image separation has been investigated. As a result, a number of feature extraction algorithms for direct application of such image structures have been developed. For example, separation of mixed fingerprints found in any crime scene, in which a mixture of two or more fingerprints may be obtained, for identification, we have to separate them. In this paper, we have proposed a new technique for separating a multiple mixed images based on exponentiated transmuted Weibull distribution. To adaptively estimate the parameters of such score functions, an efficient method based on maximum likelihood and genetic algorithm will be used. We also calculate the accuracy of this proposed distribution and compare the algorithmic performance using the efficient approach with other previous generalized distributions. We find from the numerical results that the proposed distribution has flexibility and an efficient resultComment: 14 pages, 12 figures, 4 tables. International Journal of Computer Science and Information Security (IJCSIS),Vol. 14, No. 3, March 2016 (pp. 423-433

Generalized Chaplygin Gas Models tested with SNIa

The so called Generalized Chaplygin Gas (GCG) with the equation of state $p = - \frac{A}{{\rho}^{\alpha}}$ was recently proposed as a candidate for dark energy in the Universe. In this paper we confront the GCG with SNIa data. Specifically we have tested the GCG cosmology in three different classes of models with (1) $\Omega_m= 0.3$, $\Omega_{Ch}= 0.7$; (2) $\Omega_m= 0.05$, $\Omega_{Ch}= 0.95$ and (3) $\Omega_m = 0$, $\Omega_{Ch} = 1$, as well as the model withouth any assumption on $\Omega_m$. The best fitted models are obtained by minimalizing the $\chi^2$ function and $\chi^2$ levels in the $(A_0, \alpha)$ plane. We supplemented our analysis with confidence intervals in the $(A_0, \alpha)$ plane, as well as one-dimensional probability distribution functions for models parameter. The general conclusion is that SNIa data strongly support the Chaplygin gas (with $\alpha = 1$). Extending our analysisby relaxing the flat prior lead to the result that even though the best fitted values of $\Omega_k$ are formally non-zero, still they are close to flat case. It should be viewed as an advantage of the GCG model since in similar analysisof $\Lambda$CDM model high negative value of $\Omega_{k}$ were found to be bestfitted to the data and independent inspiration from CMBR and extragalactic astronomy has been invoked to fix the curvature problem. Our results show clearly that in Generalized Chaplygin Gas cosmology distant $z >1$ supernovae should be brighter than in $\Lambda$CDM model.This prediction seems to be confirmed with new Riess high redshift SNIa sample. Moreover, we argue that with the future SNAP data it would be possible to differentiate between models with various value of $\alpha$ parameter and/or discriminated between GCG, Cardassian and $\Lambda$CDM modelsComment: 54 pages 29 figures improved version analysis flat prior relaxed high redshift Riess SNIa sample include

Generalized Hoeffding-Sobol Decomposition for Dependent Variables -Application to Sensitivity Analysis

In this paper, we consider a regression model built on dependent variables. This regression modelizes an input output relationship. Under boundedness assumptions on the joint distribution function of the input variables, we show that a generalized Hoeffding-Sobol decomposition is available. This leads to new indices measuring the sensitivity of the output with respect to the input variables. We also study and discuss the estimation of these new indices