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15 October 2019, Volume 36 Issue 5 Previous Issue    Next Issue

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Log-sum Penalized Poisson Loss Minimization for Matrix Recovery GAO Meng-meng, HAN Guo-dong, CAO Wen-fei 2019, 36 (5):  489-503.  doi: 10.3969/j.issn.1005-3085.2019.05.001 Abstract ( 172 )   PDF (659KB) ( 380 )   Save In engineering applications, including intelligent transportation systems, data mining, distance measurements etc., most of matrix recovery models are proposed based on the convex relaxation of matrix rank function, and have obtained the significant recovery performances. However, the studies of compression sensing show that the convex relaxation function has many disadvantages in the signal recovery task. In this paper, the non-convex relaxation function is thus exploited to solve the matrix recovery problem under Poisson noise. In specific, a Log-sum function regularized recovery model is introduced, and then an efficient algorithm is designed for the proposed model and its convergence result is also provided. Experimental results on the simulated and real data demonstrate that the proposed method can obtain better recovery performance compared with the existing methods. Related Articles | Metrics

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Comparison of Hybrid GEE Method and QIF Method YANG Zhuo-ran, FU Li-ya 2019, 36 (5):  504-514.  doi: 10.3969/j.issn.1005-3085.2019.05.002 Abstract ( 206 )   PDF (492KB) ( 477 )   Save Generalised estimating equations method has been widely applied to longitudinal data analysis. The resulting estimators are consistent whether the true correlation matrix is specified or misspecified. However, when the working correlation matrix is far away from the true one, the efficiency will be low. In order to reduce the influence of the choice of working correlation matrices in terms of efficiency, quadratic inference functions method and hybrid generalised estimating equations method have been proposed. In this paper, several simulation studies are conducted to compare the hybrid generalised estimating equations method with the quadratic inference functions method. Related Articles | Metrics

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A Coding Theorem for Nonhomogeneous Markov Source ZHOU Dan, WANG Zhong-zhi 2019, 36 (5):  515-524.  doi: 10.3969/j.issn.1005-3085.2019.05.003 Abstract ( 160 )   PDF (154KB) ( 249 )   Save This paper is in order to extend the memoryless discrete source coding theorem to the case of nonhomogeneous Markov chain which leads to a greater application range. Firstly, we establish a strong law of large numbers of a delayed nonhomogeneous Markov chain by the classical Borel-Cantelli lemma. Then, we apply an independent random source to approximate the nonhomogeneous Markov source in order to obtain the general coding theorem of the nonhomogeneous Markov source. Finally, with the help of the general coding theorem of nonhomogeneous Markov source, we propose the a numerical method of the lowest fault tolerance rate in batch data hypothesis test. Related Articles | Metrics

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Statistical Inference of Mixture of Generalized Linear Models YUAN Qiao-li, WU Liu-cang, DAI Lin 2019, 36 (5):  525-534.  doi: 10.3969/j.issn.1005-3085.2019.05.004 Abstract ( 239 )   PDF (190KB) ( 237 )   Save In this paper, a mixture of generalized linear model is proposed and the parameter estimation to fit the practical data is performed. Firstly, based on the existence of the first, second order moments of a heterogeneous population, the mixture of generalized linear models is applied to establish the mean model in the subpopulation, and the extended quasi-likelihood and pseudo-likelihood functions are constructed. Moreover, by using EM algorithm, the mean parameter, dispersion and mixing ratio are estimated, and Monte Carlo simulation studies are indicated the effectiveness. Finally, a real example illustrates that the model and method is scientific and useful. Related Articles | Metrics

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An Alternating Band Parallel Difference Method for Time Fractional Diffusion Equation YANG Xiao-zhong, WU Li-fei 2019, 36 (5):  535-550.  doi: 10.3969/j.issn.1005-3085.2019.05.005 Abstract ( 192 )   PDF (728KB) ( 659 )   Save The fractional anomalous diffusion equation has profound physical background and rich theoretical connotation, and its numerical methods are of important scientific significance and engineering application value. For the two-dimensional time fractional anomalous diffusion equation, an alternating band Crank-Nicolson difference parallel computing method (ABdC-N method) is studied in this paper. Based on the alternating segment technology, the ABdC-N scheme is constructed from the classic explicit scheme, implicit scheme and Crank-Nicolson difference scheme. It can be seen from both theoretical analyses and numerical experiments that the ABdC-N method is unconditionally stable and convergent. This method has good characteristics of parallel computing, and its computation efficiency is much higher than the classical serial differential method. Our results thus show that the ABdC-N difference method is effective for solving the two-dimensional time fractional anomalous diffusion equation. Related Articles | Metrics

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The Rational Approximation to $|x|^{\alpha} (1\leq \alpha<2)$ at the Adjusted Tangent Nodes CHENG Yi-yuan, ZHANG Yong-quan, ZHA Xing-xing 2019, 36 (5):  551-556.  doi: 10.3969/j.issn.1005-3085.2019.05.006 Abstract ( 126 )   PDF (137KB) ( 240 )   Save Since Newman's rational operator has a good approximation for $|x|$, we consider the approximation of $|x|^{\alpha}$ by a Newman-$\alpha$ rational operator. In this paper, we discuss the convergence rate of the operator Newman-$\alpha$ at the adjusted tangent nodes $X=\{\tan^{2}\frac{k\pi}{4n}\}_{k=1}^{n}$, and finally obtain the exact approximation order $O(\frac{1}{n^{2\alpha}})$. The result not only contains the approximation result in the case of $\alpha=1$, but it is better than the conclusion when the node group is selected for the first and the second type of Chebyshev nodes, equidistant nodes etc. Related Articles | Metrics

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Optimal Strategy with Multiple Risky Assets for DC Pension Plans under Inflation: a Market Completion Framework WANG Li-yuan, CHEN Zhi-ping, LI Zong-xin 2019, 36 (5):  557-577.  doi: 10.3969/j.issn.1005-3085.2019.05.007 Abstract ( 190 )   PDF (215KB) ( 270 )   Save The continuous-time optimal investment problem for a defined contribution (DC) pension plan under an incomplete market is considered in this paper. We take into account the inflation risk which is important but neglected in most studies. Different from many usual models, the proposed model maximizes the expected utility of the actual terminal wealth and can cope with multiple risky assets. By reducing the dimension of the underlying Brownian motions to equal to the number of risky assets, we formulate an auxiliary problem under a complete market. Applying the stochastic dynamic programming method, we derive the associated Hamilton-Jacobi-Bellman (HJB) equation, and obtain the explicit solution under the power utility function. Finally, in order to better understand our results, numerical experiments are carried out to illustrate the effects of main parameters on the optimal strategy. Related Articles | Metrics

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A Combinatorial Optimization Approach for the Competence Set Expansion Problem LIN Hao, LIN Lan 2019, 36 (5):  578-594.  doi: 10.3969/j.issn.1005-3085.2019.05.008 Abstract ( 138 )   PDF (157KB) ( 356 )   Save The optimal competence set expansion problem is to minimize the total acquiring cost in an expansion process from a set of existing skills to a set of required skills. A numerical approach based on integer programming has been developed in the literature. In this paper we establish a directed network connection model and propose a combinatorial optimization approach for the problem. The main results have been proved: 1)  the problem is strongly NP-hard;  2)  the problem can be solved in polynomial time if the number of intermediate vertices is a constant;  3)  the problem admits an  approximation algorithm of performance ratio 2. Moreover, an exact algorithm (branch-and-bound algorithm) and heuristic algorithms are provided. Related Articles | Metrics

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Empirical Likelihood for Linear Models under Strongly Mixing Samples CHEN Yu-qiu, QIN Yong-song 2019, 36 (5):  595-610.  doi: 10.3969/j.issn.1005-3085.2019.05.009 Abstract ( 130 )   PDF (142KB) ( 331 )   Save Dependent data are popular in applications. The dependence described by strong mixing  is the weakest among well-known mixing structures, which appears in many application fields such as the pricing theories of financial assets. In this paper, by applying the blockwise empirical likelihood (EL) approach, the EL-based confidence regions for the regression vector in a linear model under strongly mixing errors are established, which can be used for the interval estimation and hypothesis testing of the regression vector. Results of a small simulation study on the finite sample performance of the confidence regions are provided. Related Articles | Metrics