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DEVIATION OF THE ERROR ESTIMATION FOR VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS

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Acta Mathematica Scientia 2018年第4期38卷 1322-1344页

作者： Mohammad ZAREBNIA Reza PARVAZ Amir SABOOR BAGHERZADEH Department of Mathematics University of Mohaghegh Ardabili Department of Applied Mathematics Faculty of Mathematics Ferdowsi University of Mashhad

In this paper, we study an efficient asymptotically correction of a-posteriori er- ror estimator for the numerical approximation of Volterra integro-differential equations by piecewise polynomial collocation method. The deviation of the error for Volterra integro- differential equations by using the defect correction principle is defined. Also, it is shown that for m degree piecewise polynomial collocation method, our method provides O（hm＋l） as the order of the deviation of the error. The theoretical behavior is tested on examples and it is shown that the numerical results confirm the theoretical part.

关键词： Volterra integro-differential defect correction principle piecewise polynomial collocation finite difference error analysis

ON BAHADUR ASYMPTOTIC EFFICIENCY IN A SEMIPARAMETRIC REGRESSION MODEL

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Acta Mathematicae Applicatae Sinica 1995年第2期11卷 172-183页

作者：梁华成平 Institute of Systems Science the Chinese Academy of Science Beijing China

In this paper. the authors consider Bahadur asymptotic efficiency of LS estimators βof β, which is an unknown parameter vector in the semiparametric regression model Y=HTβ+g(T)+ε,where g is an unknown Holder continuous function, ε is a random error, X is a random vector in Rk, T is a random variable in [0,1], X and T are independent.

关键词： Bahadur efficiency semiparametric model piecewise polynomial

OPTIMAL　GLOBAL　RATES　OF　CONVERGENCE　OF　M－ESTIMATES　FOR　MULTIVARIATE　NONPARAMETRIC　REGRESSION

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Acta Mathematicae Applicatae Sinica 1995年第2期11卷 139-151页

作者：施沛德王学仁 Institute of Systems Science the Chinese Academy of Sciences Beijing China Institute of Applied Statistics Yunnan University Kunming China

Consider the nonparametric regression model Y=go(T)+u, where Y is real-valued, u is a random error, T is a random d-vector of explanatory variables ranging over a nondegenerate d-dimensional compact set C, and go(·) is the unknown smooth regression function, which is m (0) times continuously differentiable and its mth partial derivatives satisfy the Hǒlder condition with exponent γ∈(0,1], where i1, . . . , id are nonnegative integers satisfying ik=m. The piecewise polynomial estimator of go based on M-estimates is considered. It is proved that the rate of convergence of the underlying estimator is Op () under certain regular conditions, which is the optimal global rate of convergence of least square estimates for nonparametric regression studied in [10-11] .

关键词： Nonparametric regression global rate of convergence piecewise polynomial Mestimates

Asymptotic Normality of Pseudo-LS Estimator of Error Variance in Partly Linear Autoregressive Models

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Chinese Quarterly Journal of Mathematics 2006年第4期21卷 617-622页

作者： WU Xin-qian TIAN Zheng JU Yan-wei Department of Applied Mathematics Northwestern Polytechnieal University Xi＇an 710072 China National Key Laboratory of Pattern Recognition Beijing 100080 China Institute of Automation Chinese Academy of Sciences Beijing 100080China

Consider the model Yt = βYt-1＋g（Yt-2）＋εt for 3 〈 t 〈 T. Hereg is anunknown function, β is an unknown parameter, εt are i.i.d, random errors with mean 0 andvariance σ2 and the fourth moment α4, and α4 are independent of Y8 for all t ≥ 3 and s = 1, ***-LS estimators σ, σ2T α4τ and D2T of σ^2,α4 and Var（ε2↑3） are respectively constructedbased on piecewise polynomial approximator of g. The weak consistency of α4T and D2T are proved. The asymptotic normality of σ2T is given, i.e., √T（σ2T -σ^2）/DT converges indistribution to N（0, 1）. The result can be used to establish large sample interval estimatesof σ^2 or to make large sample tests for σ^2.

关键词： partly linear autoregressive model error variance piecewise polynomial pseudo-LS estimation weak consistency asymptotic normality

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关于用分段多项式逼近的逆定理的注记

浙江大学学报(理学版) 1985年第1期 12-15页

作者：来明骏

Schumaker,L.L.在[1]中证明了下述定理:定理S设[a,b]的分划序列△满足混合条件,并且稳定地趋于0,那么

关键词： approximation piecewise polynomial