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Covariate-Assisted Matrix Completion with Multiple Structural Breaks

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Journal of Systems Science & Complexity 2024年第2期37卷 692-728页

作者： MENG Jing FENG Long ZOU Changliang WANG Zhaojun School of Statistics and Data Science KLMDASRLEBPSand LPMCNankai UniversityTianjin 300071China

In matrix completion,additional covariates often provide valuable information for completing the unobserved entries of a high-dimensional low-rank matrix *** this paper,the authors consider the matrix recovery problem when there are multiple structural breaks in the coefficient matrix β under the column-space-decomposition model A=Xβ+B.A cumulative sum(CUSUM)statistic is constructed based on the penalized estimation of β.Then the CUSUM is incorporated into the Wild Binary Segmentation(WBS)algorithm to consistently estimate the location of ***,a nearly-optimal recovery of A is *** findings are further corroborated via numerical experiments and a real-data application.

关键词： Additional covariates matrix completion multiple structural breaks wild Binary Segmentation

Two-Stage Online Debiased Lasso Estimation and Inference for High-Dimensional Quantile Regression with Streaming Data

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Journal of Systems Science & Complexity 2024年第3期37卷 1251-1270页

作者： PENG Yanjin WANG Lei School of Statistics and Data Science KLMDASRLEBPS and LPMCNankai UniversityTianjin 300071China

In this paper,the authors propose a two-stage online debiased lasso estimation and statistical inference method for high-dimensional quantile regression(QR)models in the presence of streaming *** the first stage,the authors modify the QR score function based on kernel smoothing and obtain the online lasso smoothed QR estimator through iterative *** estimation process only involves the current data batch and specific historical summary statistics,which perfectly accommodates to the special structure of streaming *** the second stage,an online debiasing procedure is carried out to eliminate biases caused by the lasso penalty as well as the accumulative approximation error so that the asymptotic normality of the resulting estimator can be *** authors conduct extensive numerical experiments to evaluate the performance of the proposed *** experiments demonstrate the effectiveness of the proposed method and support the theoretical *** application to the Beijing PM2.5 Dataset is also presented.

关键词： Adaptive tuning asymptotic normality debiased lasso online updating quantile regres-sion

ON THE RENEWAL RISK MODEL WITH INTEREST AND DIVIDEND

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Acta Mathematica Scientia 2010年第5期30卷 1730-1738页

作者：房莹吴荣 Department of Mathematics and lpmc Nankai University Department of Mathematics Shangdong Normal University

We consider that the reserve of an insurance company follows a renewal risk process with interest and dividend. For this risk process, we derive integral equations and exact infinite series expressions for the Cerber-Shiu discounted penalty function. Then we give lower and upper bounds for the ruin probability. Finally, we present exact expressions for the ruin probability in a special case of renewal risk processes.

关键词： Gerber-Shiu discounted penalty function ruin probability dividend interest

On isometric extension problem between two unit spheres

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Science China Mathematics 2009年第10期52卷 2069-2083页

作者： Ding GuangGui School of Mathematical Sciences and lpmc, Nankai University, Tianjin 300071, China School of Mathematical Sciences and lpmc Nankai University Tianjin China

In this paper we introduce the isometric extension problem of isometric mappings between two unit spheres. Some important results of the related problems are outlined and the recent progress is mentioned.

关键词： normed space isometric extension isometric mapping 1-Lipschitz mapping 46A22 46B02 46B04 46B20 46B22

Brake subharmonic solutions of first order Hamiltonian systems

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Science China Mathematics 2010年第10期53卷 2719-2732页

作者： LI Chong & LIU ChunGen School of Mathematical Sciences and lpmc,Nankai University,Tianjin 300071,China School of Mathematical Sciences and lpmc Nankai University Tianjin China

In this paper,we mainly use the Galerkin approximation method and the iteration inequalities of the L-Maslov type index theory to study the properties of brake subharmonic solutions for the first order non-autonomous Hamiltonian *** prove that when the positive integers j and k satisfy the certain conditions,there exists a jT-periodic nonconstant brake solution zj such that zj and zkj are distinct.

关键词： brake subharmonic solution L-Maslov type index Hamiltonian systems

THE JOINT DISTRIBUTIONS OF SOME ACTUARIAL DIAGNOSTICS FOR THE JUMP-DIFFUSION RISK PROCESS

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Acta Mathematica Scientia 2010年第3期30卷 664-676页

作者：吕玉华吴荣徐润 Department of Mathematics Qufu Normal University School of Mathematics Sciences and lpmc Nankai University

In this article, the joint distributions of several actuarial diagnostics which are important to insurers＇ running for the jump-diffusion risk process are examined. They include the ruin time, the time of the surplus process leaving zero ultimately （simply, the ultimately leaving-time）, the surplus immediately prior to ruin, the supreme profits before ruin, the supreme profits and deficit until it leaves zero ultimately and so on. The explicit expressions for their distributions are obtained mainly by the various properties of Levy process, such as the homogeneous strong Markov property and the spatial homogeneity property etc, moveover, the many properties for Brownian motion.

关键词： Jump-diffusion risk process Brownian motion time of ruin ultimately leaving-time homogeneous strong Markov property

Convergence of Riemannian sums of inverse wavelet transforms

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Science China Mathematics 2011年第4期54卷 681-698页

作者： SUN XuDong SUN WenChang Department of Mathematics and lpmc Nankai UniversityTianjin 300071China

We study the approximation of the inverse wavelet transform using Riemannian *** show that when the Fourier transforms of wavelet functions satisfy some moderate decay condition,the Riemannian sums converge to the function to be reconstructed as the sampling density tends to *** also study the convergence of the operators introduced by the Riemannian *** result improves some known ones.

关键词： wavelet frames wavelet transforms Riemannian sums

CLASSICAL RISK MODEL WITH THRESHOLD DIVIDEND STRATEGY

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Acta Mathematica Scientia 2008年第2期28卷 355-362页

作者：周明郭军义 CIAS Central University of Finance and Economics School of Mathematical Sciences and lpmc Nankai University

In this article, a threshold dividend strategy is used for classical risk model. Under this dividend strategy, certain probability of ruin, which occurs in case of constant barrier strategy, is avoided. Using the strong Markov property of the surplus process and the distribution of the deficit in classical risk model, the survival probability for this model is derived, which is more direct than that in Asmussen（2000, P195, Proposition 1.10）. The occupation time of non-dividend of this model is also discussed by means of Martingale method.

关键词： Threshold dividend strategy ruin occupation time piecewise deterministic Markov process

A Nontrivial Product of Filtration s+5 in the Stable Homotopy of Spheres

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Acta Mathematica Sinica,English Series 2007年第3期23卷 385-392页

作者： Xiu Gui LIU Department of Mathematics and lpmc Nankai University Tianjin 300071 P. R. China

In this paper, some groups Ext A^s.t （Zp, Zp） with specialized s and t are first computed by the May spectrM sequence. Then we make use of the Adams spectral sequence to prove the existence of a new nontrivial family of filtration s＋5 in the stable homotopy groups of spheres πpnq＋（s＋3）pq＋（s＋1）q-5S which is represented （up to a nonzero scalar） by β＋2bohh∈ExtA^s＋5,P^nq＋（n＋3）pq＋（n＋1）q＋s（Zp, Zp） in the Adams spectral sequence, where p ≥ 5 is a prime number, n ≥3, 0≤ s 〈 p - 3, q = 2（p - 1）.

关键词： Stable homotopy of spheres Adams spectral sequence Toda Smith spectrum May spectral sequence