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应用数学 2024年第4期37卷 885-892页

作者： WANG Yihan ZHANG Xuekang School of Mathematics and Statistics Anhui Normal UniversityWuhu 241002China School of Mathematics-Physics and Finance Anhui Polytechnic UniversityWuhu 241000China

The present paper deals with the problem of nonparametric kernel density estimation of the trend function for stochastic processes driven by fractional Brownian motion of the second *** consistency,the rate of convergence,and the asymptotic normality of the kernel-type estimator are ***,we prove that the rate of convergence of the kernel-type estimator depends on the smoothness of the trend of the nonperturbed system.

关键词： nonparametric estimation Fractional Brownian motion Uniform consistency Asymptotic normality

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 *** using"time division",the authors overcome the problem of sample observation in time varying *** addition,the authors prove the strong consistency and limit distribution of the ***,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

nonparametric estimation for hazard rate monotonously decreasing system

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Journal of Systems Engineering and Electronics 2005年第1期16卷 220-223页

作者： HanFengyan LiWeisong SchoolofManagementEngineering BeijingUniversityofAeronauticsandAstronauticsBeijing100083P.R.China SchoolofElectronicandInformationEngineering Xi'anJiaotongUniversityXi'an710049P.R.China

estimation of density and hazard rate is very important to the reliability analysis of a system. In order to estimate the density and hazard rate of a hazard rate monotonously decreasing system, a new nonparametric estimator is put forward. The estimator is based on the kernel function method and optimum algorithm. Numerical experiment shows that the method is accurate enough and can be used in many cases.

关键词： reliability hazard rate nonparametric estimation monotonously decreasing.

nonparametric estimation for stationary and strongly mixing processes on Riemannian manifolds

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Communications in Mathematics and Statistics 2022年第4期10卷 599-621页

作者： Amour T.Gbaguidi Amoussou Freedath Djibril Moussa Carlos Ogouyandjou Mamadou Abdoul Diop IMSP Universitéd’Abomey-Calavi(UAC)DangboBenin FAST Universitéd’Abomey-CalaviAbomey-CalaviBenin UniversitéGaston Berger DakarSenegal

In this paper,nonparametric estimation for a stationary strongly mixing and manifoldvalued process(X_(j))is *** this non-Euclidean and not necessarily i.i.d setting,we propose kernel density estimators of the joint probability density function,of the conditional probability density functions and of the conditional expectations of functionals of X_(j)given the past behavior of the *** prove the strong consistency of these estimators under sufficient conditions,and we illustrate their performance through simulation studies and real data analysis.

关键词： Riemannian manifolds nonparametric estimation Kernel density estimation Stationary and strongly mixing processes Strong consistency

nonparametric estimation of Interval-censored Failure Time Data in the Presence of Informative Censoring

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Acta Mathematicae Applicatae Sinica 2017年第1期33卷 107-114页

作者： Chun-jie WANG Jian-guo SUN De-hui WANG Ning-zhong SHI The College of Basic Science Changchun University of Technology Changchun 130012 China Mathematics School and Institute of Jilin University Changchun 130012 China Department of Statistics University of Missouri 146 Middlebush Hall MO 65211. USA Key Laboratory of Applied Statistics of MOE School of Mathematics and Statistics Northeast Normal University Changchun 130024 China

nonparametric estimation of a survival function is one of the most commonly asked questions in the analysis of failure time data and for this, a number of procedures have been developed under various types of censoring structures （Kalbfleisch and Prentice, 2002）. In particular, several algorithms are available for interval-censored failure time data with independent censoring mechanism （Sun, 2006; Turnbull, 1976）. In this paper, we consider the interval-censored data where the censoring mechanism may be related to the failure time of interest, for which there does not seem to exist a nonparametric estimation procedure. It is well-known that with informative censoring, the estimation is possible only under some assumptions. To attack the problem, we take a copula model approach to model the relationship between the failure time of interest and censoring variables and present a simple nonparametric estimation procedure. The method allows one to conduct a sensitivity analysis among others.

关键词： copula models interval censored data dependent censoring nonparametric estimation

nonparametric Two-Step estimation of Drift Function in the Jump-Diffusion Model with Noisy Data

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Journal of Systems Science & Complexity 2022年第6期35卷 2398-2429页

作者： YE Xuguo ZHAO Yanyong LIN Jinguan LONG Weifang School of Science Kaili UniversityKaili 556011China Department of Statistics Nanjing Audit UniversityNanjing 211815China

This paper considers a nonparametric diffusion process whose drift and diffusion coefficients are nonparametric functions of the state variable.A two-step approach to estimate the drift function of a jump-diffusion model in noisy settings is *** proposed estimator is shown to be consistent and asymptotically normal in the presence of finite activity *** experiments and a real data application are undertaken to assess the finite sample performance of the newly proposed method.

关键词： Drift function jump-diffusion processes microstructure noise nonparametric estimation

Asymptotic properties of a nonparametric conditional density estimator in the local linear estimation for functional data via a functional single-index model

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Statistical Theory and Related Fields 2022年第3期6卷 208-219页

作者： Fadila Benaissa Abdelmalek Gagui Abdelhak Chouaf University Oran 1 Ahmed Ben Bella Oran OranAlgeria Laboratory of Statistics and Stochastic Processes Djillali Liabes UniversitySidi Bel AbbesAlgeria

This paper deals with the conditional density estimator of a real response variable given a functional random variable(i.e.,takes values in an infinite-dimensional space).Specifically,we focus on the functional index model,and this approach represents a good compromise between nonparametric and parametric *** we give under general conditions and when the variables are independent,the quadratic error and asymptotic normality of estimator by local linear method,based on the single-index ***,wecomplete these theoretical advances by some simulation studies showing both the practical result of the local linear method and the good behaviour for finite sample sizes of the estimator and of the Monte Carlo methods to create functional pseudo-confidence area.

关键词： Mean squared error single functional index conditional density function nonparametric estimation local linear estimation asymptotic normality functional data

Reducing component estimation for varying coefficient models with longitudinal data

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Science China Mathematics 2008年第2期51卷 250-272页

作者： TANG QingGuo~(1,2+) WANG JinDe~2 1 Institute of Sciences,People’s Liberation Army University of Science and Technology,Nanjing 210007,China 2 Department of Mathematics,Nanjing University,Nanjing 210093,China Institute of Sciences People’s Liberation Army University of Science and Technology Nanjing China Department of Mathematics Nanjing University Nanjing China

Varying-coefficient models with longitudinal observations are very useful in epidemiology and some other practical *** this paper,a reducing component procedure is proposed for es- timating the unknown functions and their derivatives in very general models,in which the unknown coefficient functions admit different or the same degrees of smoothness and the covariates can be time- *** asymptotic properties of the estimators,such as consistency,rate of convergence and asymptotic distribution,are *** asymptotic results show that the asymptotic variance of the reducing component estimators is smaller than that of the existing estimators when the coefficient functions admit different degrees of *** sample properties of our procedures are studied through Monte Carlo simulations.

关键词： varying coefficient model longitudinal data nonparametric estimation reducing component estimators asymptotic normality 62G07

Reweighted Nadaraya-Watson estimation of jump-diffusion models

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Science China Mathematics 2012年第5期55卷 1005-1016页

作者： HANIF Muhammad WANG HanChao LIN ZhengYan Department of Mathematics Zhejiang University

In this paper,we study the nonparametric estimation of the second infinitesimal moment by using the reweighted Nadaraya-Watson (RNW) approach of the underlying jump diffusion *** establish strong consistency and asymptotic normality for the estimate of the second infinitesimal moment of continuous time models using the reweighted Nadaraya-Watson estimator to the true function.

关键词： continuous time model Harris recurrence jump-diffusion model local time nonparametric estimation RNW estimator

Introducing System Identification Strategy into Model Predictive Control

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Journal of Systems Science & Complexity 2020年第5期33卷 1402-1421页

作者： WANG Jianhong RICARDO A.Ramirez-Mendoza JORGE de J Lozoya Santos School of Electronic Engineering and Automation Jiangri University of Science and TechnologyGanzhou343000China School of Engineering and Sciences Tecnologico de MonterreyMonterreyAve.Eugenio Garza Sada 2501MonterreyN.L.64849Merico

As system identification theory and model predictive control are belonged to two different research fields separately,so one gap exists between these two *** alleviate this gap between them,one new idea proposed in this paper is to introduce system identification theory into model predictive *** the most important element in model predictive control is the prediction of the output value for a nonlinear system,then the problem of deriving the prediction of the output value can be achieved by system identification *** specifically,a Bayesian approach is applied for the nonparametric estimation by modeling the prediction as realizations of zero mean random *** comparing this kind of prediction corresponding to this Bayesian approach and the former direct weight optimization identification for nonlinear system,the authors see that if the unknown weights are chosen appropriately,these two approaches are equivalent to each *** on the obtained prediction of the output value,the authors substitute this prediction of the output value into one cost function of model predictive control,and then a quadratic programming problem with inequality constraints is *** to solve this quadratic programming problem,a detailed process about how to derive its dual form is *** the dual problem has a simple constraint set,it is amenable to the use of the common Gauss-Seidel algorithm,whose convergence can be shown ***,one simulation example confirms the proposed theoretical results.

关键词： Equivalence model predictive control nonparametric estimation system identification