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Oracle Inequality for Sparse Trace Regression Models with Exponentialβ-mixing Errors

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Acta Mathematica Sinica,English Series 2023年第10期39卷 2031-2053页

作者： Ling PENG Xiang Yong TAN Pei Wen XIAO Zeinab RIZK Xiao Hui LIU school of statistics and data science Jiangxi University of Finance and EconomicsNanchang 330013P.R.China key laboratory of data science in finance and economics Jiangxi University of Finance and EconomicsNanchang 330013P.R.China

In applications involving,e.g.,panel data,images,genomics microarrays,etc.,trace regression models are useful *** address the high-dimensional issue of these applications,it is common to assume some sparsity *** the case of the parameter matrix being simultaneously low rank and elements-wise sparse,we estimate the parameter matrix through the least-squares approach with the composite penalty combining the nuclear norm and the *** extend the existing analysis of the low-rank trace regression with *** to exponentialβ-mixing *** explicit convergence rate and the asymptotic properties of the proposed estimator are ***,as well as a real data application,are also carried out for illustration.

关键词： Trace regression model low-rank matrix oracle inequality exponentialβ-mixing errors

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A Unit Root Test for an AR(1)Process with AR Errors by Using Random Weighted Bootstrap

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Acta Mathematica Sinica,English Series 2023年第9期39卷 1834-1854页

作者： Xiao Hui Liu Ya Wen Fan Yu Zi Liu Shi Hua Luo school of statistics and data science Jiangxi University of Finance and EconomicsNanchang330013P.R.China key laboratory of data science in finance and economics Jiangxi University of Finance and EconomicsNanchang330013P.R.China

A great deal of economic problems are related to detecting the stability of time series data,where the main interest is in the unit root *** this paper,we consider the unit root testing problem with errors being long-memory processes with the LARCH structure.A new test statistic is developed by using the random weighted bootstrap *** turns out that the proposed statistic has a chisquared distribution asymptotically regardless of the process being stationary or nonst at ionary,and with or without an intercept *** simulation results show that the statistic has a desired finite sample performance in terms of both size and power.A real data application is also given relying on the inflation rate data of 17 countries.

关键词： Autoregressive model random weighted bootstrap autoregressive errors unit root test

Statistical Inferences in a Partially Linear Model with Autoregressive Errors

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Acta Mathematicae Applicatae Sinica 2022年第4期38卷 822-842页

作者： Xiao-hui LIU Yu WANG Ya-wen FAN Yu-zi LIU school of statistics Jiangxi University of Finance and EconomicsNanchang 330013China key laboratory of data science in finance and economics Jiangxi University of Finance and EconomicsNanchang 330013China

In this paper,we consider the statistical inferences in a partially linear model when the model error follows an autoregressive process.A two-step procedure is proposed for estimating the unknown parameters by taking into account of the special structure in *** the asymptotic matrix of the estimator for the parametric part has a complex structure,an empirical likelihood function is also *** derive the asymptotic properties of the related statistics under mild *** simulations,as well as a real data example,are conducted to illustrate the finite sample performance.

关键词： partially linear model autoregressive errors two-step procedure profile empirical likelihood

Asymptotic Inference in the Random Coefficient Autoregressive Model with Time-functional Variance Noises

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Acta Mathematicae Applicatae Sinica 2024年第2期40卷 320-346页

作者： En-wen ZHU Zi-wei DENG Han-jun ZHANG Jun CAO Xiao-hui LIU Department of Mathematics and statistics Changsha University of Science and TechnologyChangsha 410114China school of Mathematics and Computational science Xiangtan UniversityXiangtan 411105China school of statistics and data science and Key Laboratory of Data Science in Finance and EconomicsJiangxi University of Finance and EconomicsNanchang 330013China

This paper considers the random coefficient autoregressive model with time-functional variance noises,hereafter the RCA-TFV *** first establish the consistency and asymptotic normality of the conditional least squares estimator for the constant *** semiparametric least squares estimator for the variance of the random coefficient and the nonparametric estimator for the variance function are constructed,and their asymptotic results are reported.A simulation study is presented along with an analysis of real data to assess the performance of our method in finite samples.

关键词： random coefficient autoregressive model time-functional variance conditional least squares semiparametric least squares

Theoretical analysis of the convergence property of a basic pigeon-inspired optimizer in a continuous search space

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science China(Information sciences) 2019年第7期62卷 90-98页

作者： Yushan ZHANG Han HUANG Hongyue WU Zhifeng HAO school of statistics and Mathematics Guangdong University of Finance and Economics Big data and Educational statistics Application laboratory Guangdong University of Finance and Economics school of Software Engineering South China University of Technology school of Mathematics and Big data Foshan University

The pigeon-inspired optimization(PIO) algorithm is a newly presented swarm intelligence optimization algorithm inspired by the homing behavior of pigeons. Although PIO has demonstrated effectiveness and superiority in numerous fields, particularly in practical engineering optimization, there have been few results concerning the theoretical foundations of PIO. This paper conducts convergence analysis of basic PIO in a continuous search space in two aspects. First, we analyze the convergence of each pigeon’s expected position using a difference equation and prove that the average position of each pigeon in the swarm will converge to the same value. To further study the stochastic global convergence property of the pigeon swarm, we apply the martingale theory to investigate the basic PIO swarm sequence, and achieve a sufficient condition to guarantee global convergence of the basic PIO. Our theoretical analysis shows that this convergence depends upon the accumulation of the minimum probability with which the pigeon swarm jumps to the global-optimal region at each iteration. The mathematical methods proposed in this study, particularly the martingale technique, also provide a new effective approach for the theoretical analysis of bio-inspired algorithms in continuous optimization.

关键词： pigeon-inspired optimization(PIO) convergence analysis martingale continuous optimization swarm intelligence

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Revised BDS test

Applied Mathematics(A Journal of Chinese Universities) 2024年第4期39卷 721-749页

作者： LUO Wen-ya BAI Zhi-dong HU Jiang WANG Chen school of data science Zhejiang University of Finance and EconomicsHangzhou 310018China

In this paper,we focus on the BDS test,which is a nonparametric test of ***,the null hypothesis H0 of it is that {u_(t)} is i.i.d.(independent and identically distributed),where {u_(t)} is a random *** BDS test is widely used in economics and finance,but it has a weakness that cannot be ignored:over-rejecting H0 even if the length T of {u_(t)} is as large as(100;2000).To improve the over-rejection problem of BDS test,considering that the correlation integral is the foundation of this test,we not only accurately describe the expectation of the correlation integral under H_(0),but also calculate all terms of the asymptotic variance of the correlation integral whose order is O(T^(-1))and O(T^(-2)),which is essential to improve the finite sample performance of BDS *** on this,we propose a revised BDS(RBDS)test and prove its asymptotic normality under *** RBDS test not only inherits all the advantages of BDS test,but also effectively corrects the over-rejection problem of it,which can be fully confirmed by the simulation results we ***,based on the simulation results,we find that similar to BDS test,RBDS test would also be affected by the parameter estimations of the ARCH-type model,resulting in size distortion,but this phenomenon can be alleviated by the logarithmic transformation preprocessing of the estimate residuals of the ***,through some actual datasets that have been demonstrated to fit well with ARCH-type models,we also compared the performance of BDS test and RBDS test in evaluating the goodness-of-fit of the model in empirical problem,and the results reflect that,under the same condition,the performance of the RBDS test is more encouraging.

关键词： independence the correlation integral over-rejection BDS test

Sliced Average Variance Estimation for Tensor data

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Acta Mathematicae Applicatae Sinica 2024年第3期40卷 630-655页

作者： Chuan-quan LI Pei-wen XIAO Chao YING Xiao-hui LIU school of statistics Jiangxi University of Finance and EconomicsNanchang 330013China key laboratory of data science in finance and economics Jiangxi University of Finance and EconomicsNanchang 330013China Biostatistics and Medical Informatics University of Wisconsin MadisonMadison 53726USA

Tensor data have been widely used in many fields,e.g.,modern biomedical imaging,chemometrics,and economics,but often suffer from some common issues as in high dimensional *** to find their low-dimensional latent structure has been of great interest for *** this end,we develop two efficient tensor sufficient dimension reduction methods based on the sliced average variance estimation(SAVE)to estimate the corresponding dimension reduction *** first one,entitled tensor sliced average variance estimation(TSAVE),works well when the response is discrete or takes finite values,but is not■consistent for continuous response;the second one,named bias-correction tensor sliced average variance estimation(CTSAVE),is a de-biased version of the TSAVE *** asymptotic properties of both methods are derived under mild *** and real data examples are also provided to show the superiority of the efficiency of the developed methods.

关键词： tensor data sliced average variance estimation sufficient dimension reduction central subspace

Column-orthogonal designs with multi-dimensional stratifications

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science China Mathematics 2021年第6期64卷 1291-1304页

作者： Xue Yang Jian-Feng Yang Min-Qian Liu Qi Zhou school of statistics Tianjin University of Finance and EconomicsTianjin 300222China school of statistics and data science LPMC&KLMDASRNankai UniversityTianjin 300071China

The orthogonal Latin hypercube design and its relaxation,and column-orthogonal design,are two kinds of orthogonal designs for computer ***,they usually do not achieve maximum stratifications in multi-dimensional *** this paper,we propose some methods to construct column-orthogonal designs with multi-dimensional stratifications by rotating symmetric and asymmetric orthogonal *** newly constructed column-orthogonal designs ensure that the estimates of all linear effects are uncorrelated with each other and even uncorrelated with the estimates of all second-order effects(quadratic effects and bilinear effects)when the rotated orthogonal arrays have strength larger than *** orthogonality,the resulting designs also preserve better space-filling properties than those constructed by using the existing *** addition,we provide a method to construct a new class of orthogonal Latin hypercube designs with multi-dimensional stratifications by rotating regular factorial *** newly constructed orthogonal Latin hypercube designs are tabulated for practical use.

关键词： computer experiment Latin hypercube design orthogonal array orthogonality rotation matrix

CONSTRUCTION OF IMPROVED BRANCHING LATIN HYPERCUBE DESIGNS

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Acta Mathematica Scientia 2021年第4期41卷 1023-1033页

作者： Hao CHEN Jinyu YANG Min-Qian LIU school of statistics Tianjin University of Finance and EconomicsTianjin 300222China school of statistics and data science LPMC&KLMDASRNankai UniversityTianjin 300071China

In this paper,we propose a new method,called the level-collapsing method,to construct branching Latin hypercube designs(BLHDs).The obtained design has a sliced structure in the third part,that is,the part for the shared factors,which is desirable for the qualitative branching *** construction method is easy to implement,and(near)orthogonality can be achieved in the obtained BLHDs.A simulation example is provided to illustrate the effectiveness of the new designs.

关键词： Branching and nested factors computer experiment Gaussian process model orthogonality