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asymptotic and stable properties of general stochastic functional differential equations

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Journal of Systems Engineering and Electronics 2014年第1期25卷 138-143页

作者： Xiaojing Zhong Feiqi Deng College of Automation Science and Engineering South China University of Technology

The asymptotic and stable properties of general stochastic functional differential equations are investigated by the multiple Lyapunov function method, which admits non-negative up-per bounds for the stochastic derivatives of the Lyapunov functions, a theorem for asymptotic properties of the LaSal e-type described by limit sets of the solutions of the equations is obtained. Based on the asymptotic properties to the limit set, a theorem of asymptotic stability of the stochastic functional differential equations is also established, which enables us to construct the Lyapunov functions more easily in application. Particularly, the wel-known classical theorem on stochastic stability is a special case of our result, the operator LV is not required to be negative which is more general to fulfil and the stochastic perturbation plays an important role in it. These show clearly the improvement of the traditional method to find the Lyapunov functions. A numerical simulation example is given to il ustrate the usage of the method.

关键词： stochastic functional differential equations Lyapunov functions LaSalle asymptotic properties stability semi-martingale convergence theorem.

Robust Error Density Estimation in Ultrahigh Dimensional Sparse Linear Model

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Acta Mathematica Sinica,English Series 2022年第6期38卷 963-984页

作者： Feng ZOU Heng Jian CUI School of Mathematical Sciences Capital Normal UniversityBeijing 100048P.R.China

This paper focuses on error density estimation in ultrahigh dimensional sparse linear model,where the error term may have a heavy-tailed distribution.First,an improved two-stage refitted crossvalidation method combined with some robust variable screening procedures such as RRCS and variable selection methods such as LAD-SCAD is used to obtain the submodel,and then the residual-based kernel density method is applied to estimate the error density through LAD regression.Under given conditions,the large sample properties of the estimator are also established.Especially,we explicitly give the relationship between the sparsity and the convergence rate of the kernel density estimator.The simulation results show that the proposed error density estimator has a good performance.A real data example is presented to illustrate our methods.

关键词： Ultrahigh dimensional sparse linear model robust density estimation refitted crossvalidation method asymptotic properties

Closed-loop subspace identification algorithm based on correlation function estimates

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Science China(Information Sciences) 2015年第3期58卷 173-182页

作者： WANG Jia MILLER Daniel WANG HongWei GU Hong Department of Biotechnology Dalian Medical University School of Control Science and Engineering Dalian University of Technology Department of Mechanical Engineering University of California San Diego

A novel subspace identification method based on correlation function which estimates a state-space system dynamics of unknown plant operating in closed-loop experimental condition is proposed in this paper.It is shown that the cross-correlation function of the output and external input signals are equal to the crosscorrelation function of the input and external signals filtered through the system dynamics since noise signal has no correlation with the external input.The proposed algorithm is developed to obtain unbiased estimates of system matrices based on time-shifted invariance of the correlation function estimates.Later the algorithm is compared to other popular subspace methods in the simulation study and the results show the effectiveness of our method in the presence of colored noise and low signal-to-noise ratios.

关键词： subspace identification method correlation function estimates closed-loop system asymptotic properties the system dynamics

Nonparametric Estimation for the Diffusion Coefficient of Multidimensional Time-Varying Diffusion Processes

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Journal of Systems Science & Complexity 2020年第5期33卷 1602-1631页

作者： WANG Jun CHEN Ping Department of Science Nanjing University of Science andTechnologyNanjing 210000China

This paper proposes a kernel estimator for the coefficient of multidimensional time-varying diffusion processes as an extension of the estimation model for one dimensional diffusion coefficient to the multidimensional case.By using"time division",the authors overcome the problem of sample observation in time varying model.In addition,the authors prove the strong consistency and limit distribution of the estimator.Finally,the authors test the performance of the estimator through a simulation experiment and an empirical application.

关键词： asymptotic properties kernel function multidimensional model nonparametric estimation time-inhomogeneous

QMLE for Periodic Time-Varying Asymmetric log GARCH Models

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Communications in Mathematics and Statistics 2021年第3期9卷 273-297页

作者： Ahmed Ghezal Departement de Mathematiques Universite Constantine 1ConstantineAlgeria

This paper establishes probabilistic and statistical properties of the extension of timeinvariant coefficients asymmetric log GARCH processes to periodically time-varying coefficients(P logGARCH)one.In thesemodels,the parameters of log−volatility are allowed to switch periodically between different seasons.The main motivations of this newmodel are able to capture the asymmetry and hence leverage effect,in addition,the volatility coefficients are not a subject to positivity constraints.So,some probabilistic properties of asymmetric P log GARCH models have been obtained,especially,sufficient conditions ensuring the existence of stationary,causal,ergodic(in periodic sense)solution and moments properties are given.Furthermore,we establish the strong consistency and the asymptotic normality of the quasi-maximum likelihood estimator(QMLE)under extremely strong assumptions.Finally,we carry out a simulation study of the performance of the QML and the P log GARCH is applied to model the crude oil prices of Algerian Saharan Blend.

关键词： QML Periodicity Asymmetric log GARCH EGARCH Stationarity asymptotic properties

Convergence rate of principal component analysis with local-linear smoother for functional data under a unified weighing scheme

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Statistical Theory and Related Fields 2020年第1期4卷 55-65页

作者： Xingyu Yan Xiaolong Pu Yingchun Zhou Xiaolei Xun Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOESchool of StatisticsEast China Normal UniversityShanghaiPeople’s Republic of China School of Data Science Fudan UniversityShanghaiPeople’s Republic of China

The unified weighing scheme for the local-linear smoother in analysing functional data can deal with data that are dense,sparse or of neither type.In this paper,we focus on the convergence rate of functional principal component analysis using this method.Almost sure asymptotic consistency and rates of convergence for the estimators of eigenvalues and eigenfunctions have been established.We also provide the convergence rate of the variance estimation of the measurement error.Based on the results,the number of observations within each curve can be of any rate relative to the sample size,which is consistent with the earlier conclusions about the asymptotic properties of the mean and covariance estimators.

关键词： Functional principal components asymptotic properties local-linear smoothing weighing scheme

Strong Approximations of Martingale Vectors and Their Applications in Markov-Chain Adaptive Designs

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Acta Mathematicae Applicatae Sinica 2004年第2期20卷 337-352页

作者： Li-xinZhang DepartmentofMathematics ZhejiangUniversityHangzhou310028China

The strong approximations of a class of R^d-valued martingales are considered.The conditions usedin this paper are easier to check than those used in [3] and [9].As an application,the strong approximation ofa class of non-homogenous Markov chains is established,and the asymptotic properties are established for themulti-treatment Markov chain adaptive designs in clinical trials.

关键词： Martingale Non-homogenous Markov chain Wiener processes strong approximation adaptive designs asymptotic properties

Statistical estimation in partially nonlinear models with random effects

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Statistical Theory and Related Fields 2017年第2期1卷 227-233页

作者： Ye Que Zhensheng Huang Riquan Zhang School of Science Nanjing University of Science and TechnologyNanjingP.R.China School of Finance Huainan Normal UniversityHuainanP.R.China School of Statistics East China Normal UniversityShanghaiP.R.China

In this article, a partially nonlinear model with random effects is proposed and its new estimation procession is provided. In order to estimate the link function, we propose generalised leastsquare estimate and B-splines estimate methods. Further, we also use the Gauss–Newton methodto construct the estimates of unknown parameters. Finally, we also consider the estimation forthe variance components. The consistency and the asymptotic normality of the estimator will beproved. Simulated and real examples are given to illustrate our proposed methodology, whichshows that our methods give effective estimation.

关键词： asymptotic properties B-splines method Gauss–Newton method mixed-effects models partially nonlinear models

Marginal Accelerated Hazard Model with Multivariate Failure Time Data

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Wuhan University Journal of Natural Sciences 2012年第3期17卷 185-189页

作者： YANG Qinglong LIU Yanyan School of Mathematics and Statistics Wuhan UniversityWuhan 430072HubeiChina

Multivariate failure time data are frequently encountered in biomedical research.In this article,we model marginal hazards with accelerated hazards model to analyze multivariate failure time data.Estimating equations are derived analogous to generalized estimating equation method.Under certain regular conditions,the resultant estimators for the regression parameters are shown to be asymptotically normal.Furthermore,we also establish the weak convergence of estimators for the baseline cumulative hazard functions.

关键词： multivariate failure time data marginal hazard generalized estimating equation asymptotic properties