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15 December 2018, Volume 35 Issue 6 Previous Issue    Next Issue

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Optimal Hedging Ratio of Portfolio under the R-vine Pair Copula Model CHEN Tao, CHENG Xi-jun, MA Li-jun, FU Yong-jian 2018, 35 (6):  611-621.  doi: 10.3969/j.issn.1005-3085.2018.06.001 Abstract ( 167 )   PDF (255KB) ( 452 )   Save At present, Chinese security market is not mature and risk hedging tools are limited. Therefore, the use of one futures hedging on multiple assets is an important strategy in portfolio risk management. This paper first constructs a minimum CVaR\,(Conditional Value at Risk) hedging model based on linear programming and then applies the R-vine Pair Copula-GARCH model combined with Monte Carlo simulation to generate the joint distribution of returns and scenarios that fit the simulated distribution, which is the inputs to the minimum CVaR model to obtain the optimal hedging ratio. Empirical researches based on CSI 300 stock index futures and five stocks have shown that portfolios hedged by using the proposed model in this paper achieve better performance in both return and risk control when compared with the improved hedging model under normal distribution assumption. Related Articles | Metrics

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Error Estimation of Census Content Based on Ratio Estimators HU Gui-hua, QI Li, WU Ting, LIAO Jin-pen 2018, 35 (6):  622-634.  doi: 10.3969/j.issn.1005-3085.2018.06.002 Abstract ( 191 )   PDF (217KB) ( 254 )   Save At present, departments of government statistics in many countries generally pay attention to coverage error estimation, but neglect or even eliminate content error estimation. In order to improve this situation, this paper is the first to systematically study the four evaluation indexes through sampling estimation and field verification, namely, consistency rate, net difference rate, inconsistency index, and total inconsistency index, which are used to estimate census content errors. First, the census population registration list, the quality assessment survey population registration list, the matched population registration list from the same small census area, and the sampling weights of the sample small census areas are used to construct the estimator of each evaluation index and its sampling variance estimator based on the Jack-knife method. Secondly, the calculation processes of evaluation indicators are demonstrated through a real case. Finally, the conclusion of the study is given: each evaluation index does not cover all content errors; improving the quality of matching work is the key to ensure the accuracy of content error assessment; we should pay attention to the comparability of horizontal and vertical comparison of content errors. This paper can optimize the census quality evaluation scheme of government statistics department, and improve the accuracy of census content error estimation. Related Articles | Metrics

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Optimization Algorithm and Robustness for the Models of the Center of Corneal Curvature in Gaze Tracking System XUE Xiao-na, GAO Shu-ping, HUANG Liu-yu, ZHANG Bao-yu 2018, 35 (6):  635-647.  doi: 10.3969/j.issn.1005-3085.2018.06.003 Abstract ( 143 )   PDF (894KB) ( 289 )   Save To efficiently obtain the corneal curvature center of the three-dimentional (3D) gaze tracking technology and make the system satisfy the requirements of real-time accuracy and stability, two kinds of corneal curvature center models and the solution method are proposed in this paper. Firstly, two models, nonlinear equations model and the improved model, are established to solve the center by using optic theory and the characteristics of eyeballs. Secondly, in order to quickly solve these two models, a new hybrid algorithm (GA-LM) based on genetic algorithm and LM algorithm is constructed. Finally, numerical experiments show that the proposed models and GA-LM are effective, which can quickly and accurately obtain the corneal curvature center in the 3D gaze tracking system. Related Articles | Metrics

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Noisy Image Blind Deblurring via Hyper Laplacian Prior and Spectral Properties of Convolution Kernel YU Yi-bin, WU Cheng-xin, PENG Nian, YUAN Shi-fang 2018, 35 (6):  648-654.  doi: 10.3969/j.issn.1005-3085.2018.06.004 Abstract ( 139 )   PDF (649KB) ( 344 )   Save Most of blind deblurring methods are sensitive to image noise. Even a small amount of noise can degrade the quality of restoration image dramatically. Considering that blurry image contains both blur kernel information and clear image information implicitly, we employ a prior of convolutional kernel spectral, in combination with a hyper Laplacian prior of clear image in gradient domain, to establish optimization model for blind noisy image deblurring. This model is more reasonable than other models which do not make full use of the blurry image information, so our model can obtain more accurate estimation image. In this paper, the Hessian matrix is employed to generate a prior term by using the blurry image and a blur kernel together instead of just the clear image. The proposed model can be solved by an iterative scheme which alternatively refines the blur kernel and the estimation image. At the latent image restoration stage, the variable splitting method is adopted to calculate the clear image because of the hyper Laplacian prior term. Furthermore, clear images are obtained by using fast Fourier transformation and closed-form threshold formulas to speed up the optimization process. Experimental results show that, compared with other methods, the proposed method can obtain more robust blur kernel and more accurate clear image, and the convergence speed is faster. Related Articles | Metrics

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Optimal Designs of Heteroscedastic Random Coefficient Regression Models CHENG Jing, YUE Rong-xian, QIN Zhi-yong 2018, 35 (6):  655-662.  doi: 10.3969/j.issn.1005-3085.2018.06.005 Abstract ( 167 )   PDF (149KB) ( 419 )   Save The optimal design method has been widely used in the fields of engineering, and industrial and agricultural production. The study about optimal designs of random coefficient regression model is often done under the assumption that random errors are homoscedastic, but random errors are usually related to observation points and thus have heteroscedasticity. We consider the optimal approximate design of heteroscedastic random coefficient regression model on the closed intervals in this paper. Sufficient conditions are established to ensure that the optimal designs can be achieved at two extreme points of the design region. Equal-weight design on the extreme points of symmetrical design region is proved to be multiple optimal for the random coefficient regression model with symmetrical heteroscedastic errors. It doesn't depend on the heteroscedastic structure or variances of random coefficients in the model. Related Articles | Metrics

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The Singular Perturbation Solution to Dust Plasma Diffusion Problem in Atmosphere WANG Wei-gang, MO Jia-qi 2018, 35 (6):  663-672.  doi: 10.3969/j.issn.1005-3085.2018.06.006 Abstract ( 218 )   PDF (166KB) ( 588 )   Save In order to efficiently control polluted air of dust particles and to improve the quality of ambient air, it is necessary to examine the distribution of the dust particles. In this paper, we consider a class of nonlinear diffusion equation initial value problem for the dust plasma diffusion equation in atmosphere. Firstly, the outer and initial corrective layer terms are obtained respectively by using the singular perturbation method and Fourier transformation. And the formally asymptotic expansion of solution is constructed. Secondly, using the prior estimate theory, the uniformly validity for expansion is proved. Then the any orders of asymptotic approximate solutions are derived. Finally, the physical meaning of the approximate analytic solution is investigated. From the approximate function, we can compute the correlative physical quantity of dust plasma, which can help us to adopt appropriate measures and to reduce the impact of disaster. Related Articles | Metrics

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Nonmonotone Spectral Projection Gradient Method for Solving Generalized Lyapunov Equations YU Si-ting, LI Chun-mei, DUAN Xue-feng 2018, 35 (6):  673-683.  doi: 10.3969/j.issn.1005-3085.2018.06.007 Abstract ( 141 )   PDF (212KB) ( 264 )   Save In this paper, we consider the positive semidefinite solution to a class of generalized Lyapunov matrix equation, which arises in bilinear systems. Based on the good property that the local minimizer of a convex function is also the global minimizer, the positive semidefinite solution of the generalized Lyapunov equation is transformed into a convex optimization problem. By using the nonmonotone line search technique, we develop a nonmonotone spectral projected gradient method to solve this equivalent problem. Finally, numerical examples are presented to illustrate the feasibility and effectiveness of the new method. Related Articles | Metrics

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Jacobi Collocation Method for Time Fractional Fokker-Planck Equations ZHOU Qin, YANG Yin 2018, 35 (6):  684-692.  doi: 10.3969/j.issn.1005-3085.2018.06.008 Abstract ( 153 )   PDF (258KB) ( 429 )   Save Fractional partial differential equations have recently been applied in various areas of engineering, science, finance, applied mathematics, bioengineering and others. In this paper, we convert the time fractional Fokker-Planck equation into equivalent integral equations with singular kernel, then the model solution is discretized in time and space with a spectral expansion of the Lagrange interpolation polynomial. Numerical results demonstrate the spectral accuracy and efficiency of the collocation spectral method. The proposed technique is not only easy to implement, but also can be easily extended to multidimensional problems. Related Articles | Metrics

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Compact Finite Difference Schemes for the Dissipative Nonlinear Schrödinger Equation WANG Ting-chun, ZHANG Wen, WANG Guo-dong 2018, 35 (6):  693-706.  doi: 10.3969/j.issn.1005-3085.2018.06.009 Abstract ( 124 )   PDF (186KB) ( 683 )   Save In this paper, two compact finite difference schemes are proposed and analyzed for solving a dissipative nonlinear Schrödinger equation. Due to the difficulty in obtaining the a priori estimate of numerical solutions, it is hard to prove the convergence of the proposed schemes. In order to overcome the difficulty, we truncate the coefficient function of the nonlinear term into a global Lipschitz continuous function and use the standard energy method to establish the optimal error estimates of numerical solutions in terms of the maximum norm without any restriction on the grid ratio. The convergence rates are proved to be of the fourth-order in space and the second-order in time, respectively. Numerical results support the theoretical analysis and show the advantages of the proposed schemes compared with the existing ones. Related Articles | Metrics

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Estimation of the Separation Degree of Regular Periodic Matrix Pairs LI Qing, CHEN Xiao-shan 2018, 35 (6):  707-721.  doi: 10.3969/j.issn.1005-3085.2018.06.010 Abstract ( 147 )   PDF (174KB) ( 246 )   Save The regular periodic matrix pair has some important applications in the analysis and design of linear discrete time periodic control systems. The separation degree between two regular periodic matrix pairs is an important quantity that measures the sensitivity of periodic deflating subspaces of regular periodic matrix pairs. So it is important to compute this quantity. However, this requires a lot of floating point arithmetic operations. Up to now, there are two different methods for estimating the separation degree of two matrices or two regular matrix pairs. One is based on the Schur decomposition of a matrix, the other is based on the Jordan decomposition of a matrix. In this paper, we apply the periodic Schur decompositions of regular periodic matrix pairs to derive lower and upper bounds of the separation degree. Comparing with the exact separation degree computation, estimating these bounds requires much less floating point arithmetic operations. In addition, these lower and upper bounds can be regarded as a generalization of those of the separation degree for two regular matrix pairs. Finally, lower and upper bounds are illustrated by a numerical example. Related Articles | Metrics

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An Operator Splitting Method for Image Inpainting Based on the Allen-Cahn Equation QIAO Yuan-yang, ZHAI Shu-ying, FENG Xin-long 2018, 35 (6):  722-732.  doi: 10.3969/j.issn.1005-3085.2018.06.011 Abstract ( 192 )   PDF (794KB) ( 560 )   Save In this paper, we propose an operator splitting method for image inpainting, based on the Allen-Cahn (AC) equation. The core idea is using an operator splitting method to decompose the original problem into a linear equation and a nonlinear equation. The linear equation and the nonlinear equation are solved by the finite difference Crank-Nicolson scheme and analytical method, respectively. So both time and space accuracy can achieve the second order. The method is only applied in the inpainting domain, while the pixel values of the rest region are kept as those in the original input image, which can improve the computational efficiency greatly. Accuracy and validity of the proposed method is illustrated through numerical experiments on synthetic and actual images. Related Articles | Metrics