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AN EXTENDED BLOCK RESTRICTED ISOMETRY PROPERTY FOR SPARSE RECOVERY WITH NON-GAUSSIAN NOISE

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Journal of Computational Mathematics 2020年第6期38卷 827-838页

作者： Klara Leffler Zhiyong Zhou Jun Yu department of Mathematics and Mathematical statistics Umea UniversityUmeaSweden. department of statistics Zhejiang University City CollegeHangzhou 310015China department of Mathematics and Mathematical statistics Umea UniversityUmeaSweden

We study the recovery conditions of weighted mixedl2/lp minimization for block sparse signal reconstruction from compressed measurements when partial block support information is *** show theoretically that the extended block restricted isometry property can ensure robust recovery when the data fidelity constraint is expressed in terms of anlq norm of the residual error,thus establishing a setting wherein we are not restricted to Gaussian measurement *** illustrate the results with a series of numerical experiments.

关键词： Compressed sensing Block sparsity Partial support information Signal reconstruction Convex optimization

Fast algorithms for singular value decomposition and the inverse of nearly low-rank matrices

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National Science Review 2023年第6期10卷 24-27页

作者： Chen Xu Weiwei Xu Kaili Jing department of Mathematics and statistics University of Ottawa School of Mathematics and statistics Xi'an Jiao Tong University School of Mathematics and statistics Nanjing University of Information Science and Technology

PROBLEM Matrix computation is a fundamental task in science and engineering;it is recognized as one of the seven computational’giants’of massive data analysis [1],analogous to the seven’dwarfs’in highperformance *** recent years,as the scale of datasets rapidly grows,analysts and engineers frequently need to deal with big matrices with a nearly lowrank *** big size of a matrix brings great numerical hurdles to matrix *** this work,we focus on two typical tasks in matrix computation:singular value decomposition (SVD) and matrix inverse on nearly low-rank matrices that are potentially of big sizes.

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On the rate of complete convergence for weighted sums of NSD random variables and an application

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Applied Mathematics(A Journal of Chinese Universities) 2017年第3期32卷 270-280页

作者： NADERI Habib AMINI Mohammad BOZORGNIA Abolghasem department of statistics Faculty of Mathematical Sciences Ferdowsi University of Mashhad MashhadIran department of statistics Faculty of Mathematical Sciences University of Sistan and BaluchestanZahedan Iran department of statistics Khayyam University Mashhad Iran

In this paper, the complete convergence is established for the weighted sums of negatively superadditive-dependent random variables. As an application, the Marcinkiewicz-Zygmund strong law of large numbers for the random weighted average is also achieved, and a simulation study is done for the asymptotic behaviour of random weighting estimator.

关键词： complete convergence negatively superadditive-dependent random weighted estimate

On nonparametric change point estimator based on empirical characteristic functions

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Science China Mathematics 2016年第12期59卷 2463-2484页

作者： TAN ChangChun SHI XiaoPing SUN XiaoYing WU YueHua School of Mathematics Hefei University of Technology department of Mathematics and statistics Thompson Rivers University department of Mathematics and statistics York University

We propose a nonparametric change point estimator in the distributions of a sequence of independent observations in terms of the test statistics given by Huˇskov′a and Meintanis(2006) that are based on weighted empirical characteristic functions. The weight function ω(t; a) under consideration includes the two weight functions from Huˇskov′a and Meintanis(2006) plus the weight function used by Matteson and James(2014),where a is a tuning parameter. Under the local alternative hypothesis, we establish the consistency, convergence rate, and asymptotic distribution of this change point estimator which is the maxima of a two-side Brownian motion with a drift. Since the performance of the change point estimator depends on a in use, we thus propose an algorithm for choosing an appropriate value of a, denoted by a_s which is also justified. Our simulation study shows that the change point estimate obtained by using a_s has a satisfactory performance. We also apply our method to a real dataset.

关键词： change point estimator empirical characteristic function tuning parameter convergence rate asymptotic distribution

Identifying the limiting distribution by a general approach of Stein's method

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Science China Mathematics 2016年第12期59卷 2379-2392页

作者： SHAO Qi-Man ZHANG Zhuo-Song department of statistics The Chinese University of Hong Kong

A general exchange pair approach is developed to identify the limiting distribution for any sequence of random variables, by calculating the conditional mean and the conditional second moments. The error of approximation is also studied. In particular, a Berry-Esseen type bound of O(n^(-3/4)) is obtained for the Curie-Weiss model at the critical temperature.

关键词： Stein's method exchangeable pair limiting distribution Berry-Esseen bounds Curie-Weiss model

Strong Laws of Large Numbers for Double Sums of Banach Space Valued Random Elements

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Acta Mathematica Sinica,English Series 2019年第5期35卷 583-596页

作者： Robert PARKER Andrew ROSALSKY department of Biostatistics University of Florida department of statistics University of Florida

For a double array {V_(m,n), m ≥ 1, n ≥ 1} of independent, mean 0 random elements in a real separable Rademacher type p(1 ≤ p ≤ 2) Banach space and an increasing double array {b_(m,n), m ≥1, n ≥ 1} of positive constants, the limit law ■ and in L_p as m∨n→∞ is shown to hold if ■ This strong law of large numbers provides a complete characterization of Rademacher type p Banach spaces. Results of this form are also established when 0 < p ≤ 1 where no independence or mean 0 conditions are placed on the random elements and without any geometric conditions placed on the underlying Banach space.

关键词： Real separable Banach space double array of independent random elements strong law of large numbers almost sure convergence Rademacher type p Banach space convergence in Lp

Optimal operating policy for a controllable queueing model with a fuzzy environment

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2009年第2期10卷 311-318页

作者： Chuen-horng LIN Jau-chuan KE department of Information Management department of Applied statistics National Taichung Institute of Technology

We construct the membership functions of the fuzzy objective values of a controllable queueing model,in which cost elements,arrival rate and service rate are all fuzzy numbers. Based on Zadeh's extension principle,a set of parametric nonlinear programs is developed to find the upper and lower bounds of the minimal average total cost per unit time at the possibility level. The membership functions of the minimal average total cost are further constructed using different values of the possibility level. A numerical example is solved successfully to illustrate the validity of the proposed approach. Because the object value is expressed and governed by the membership functions,the optimization problem in a fuzzy environment for the controllable queueing models is represented more accurately and analytical results are more useful for system designers and practitioners.

关键词： Controllable queue Fuzzy sets Membership function Nonlinear programming

Numerical Study of Mixed Convective Peristaltic Flow through Vertical Tube with Heat Generation for Moderate Reynolds and Wave Numbers

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Communications in Theoretical Physics 2018年第4期69卷 449-460页

作者： Tariq Javed B.Ahmed M.Sajid department of Mathematics and statistics International Islamic University

The current study focuses on the numerical investigation of the mixed convective peristaltic mechanism through a vertical tube for non-zero Reynolds and wave number. In the set of constitutional equations, energy equation contains the term representing heat generation parameter. The problem is formulated by dropping the assumption of lubrication theory that turns the model mathematically into a system of the nonlinear partial differential equations. The results of the long wavelength in a creeping flow are deduced from the present analysis. Thus, the current study explores the neglected features of peristaltic heat flow in the mixed convective model by considering moderate values of Reynolds and wave numbers. The finite element based on Galerkin's weighted residual scheme is applied to solve the governing equations. The computed solution is presented in the form of contours of streamlines and isothermal lines, velocity and temperature profiles for variation of different involved parameters. The investigation shows that the strength of circulation for stream function increases by increasing the wave number and Reynolds number. Symmetric isotherms are reported for small values of time-mean flow. Linear behavior of pressure is noticed by vanishing inertial forces while the increase in pressure is observed by amplifying the Reynolds number.

关键词： mixed convection peristaltic flow moderate Reynolds number finite element method

Variable selection procedures from multiple testing

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Science China Mathematics 2019年第4期62卷 771-782页

作者： Baoxue Zhang Guanghui Cheng Chunming Zhang Shurong Zheng School of statistics Capital University of Economics and Business School of Mathematics and statistics and Key Laboratory of Applied statistics of Ministry of Education Northeast Normal University department of statistics University of Wisconsin-Madison

Variable selection has played an important role in statistical learning and scienti?c discoveries during the past ten years, and multiple testing is a fundamental problem in statistical inference and also has wide applications in many scienti?c ?elds. Signi?cant advances have been achieved in both areas. This study attempts to ?nd a connection between the adaptive LASSO(least absolute shrinkage and selection operator) and multiple testing procedures in linear regression models. We also propose procedures based on multiple testing methods to select variables and control the selection error rate, i.e., the false discovery rate. Simulation studies demonstrate that the proposed methods show good performance relative to controlling the selection error rate under a wide range of settings.

关键词： variable selection multiple testing adaptive LASSO false discovery rate linear regression