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| 1 | ASYMPTOTIC NORMALITY OF M-ESTIMATES IN THE EV MODEL显示文摘The M-estimate of parameters in the errors-in-variables (EV) model Y =xτβ0+∈,X =x+u ((∈,uτ)τ is a (p+1)-dimensional spherical error, Coy[(∈, uτ)τ] =σ2Ip+1)being considered. The M-estimate βn,, of β0 under a general ρ(·) function and the estimateof σ2 are given, the strong consistency and asymptotic normality of βn as well as are obtained. The conditions for the ρ(·) function in this paper are similar to that of linearexpression of M-estimates in the linear regression model. | CUI Hengjian(Department of Mathematics, Beijing Normal University, Beijing 100875, China) | 1997 | Systems Science and Mathematical Sciences1997，10，3： | 16 |
| 2 | Estimation in partial linear EV models with replicated observations显示文摘The aim of this work is to construct the parameter estimators in the partial linear errors-in-variables (EV) models and explore their asymptotic properties. Unlike other related References, the assumption of known error covariance matrix is removed when the sample can be repeatedly drawn at each designed point from the model. The estimators of interested regression parameters, and the model error variance, as well as the nonparametric function, are constructed. Under some regular conditions, all of the estimators prove strongly consistent. Meanwhile, the asymptotic normality for the estimator of regression parameter is also presented. A simulation study is reported to illustrate our asymptotic results. | CUI Hengjian | 2004 | Science China Mathematics2004，47，1： | 9 |
| 3 | Robust estimation for partially linear models with large-dimensional covariates显示文摘We are concerned with robust estimation procedures to estimate the parameters in partially linear models with large-dimensional covariates. To enhance the interpretability, we suggest implementing a nonconcave regularization method in the robust estimation procedure to select important covariates from the linear component. We establish the consistency for both the linear and the nonlinear components when the covariate dimension diverges at the rate of o(n1/2), where n is the sample size. We show that the robust estimate of linear component performs asymptotically as well as its oracle counterpart which assumes the baseline function and the unimportant covariates were known a priori. With a consistent estimator of the linear component, we estimate the nonparametric component by a robust local linear regression. It is proved that the robust estimate of nonlinear component performs asymptotically as well as if the linear component were known in advance.Comprehensive simulation studies are carried out and an application is presented to examine the fnite-sample performance of the proposed procedures. | ZHU LiPing LI RunZe CUI HengJian | 2013 | Science China Mathematics2013，56，10： | 5 |
| 4 | Asymptotic distributions in the projection pursuit based canonical correlation analysis显示文摘In this paper, associations between two sets of random variables based on the projection pursuit (PP) method are studied. The asymptotic normal distributions of estimators of the PP based canonical correlations and weighting vectors are derived. | JIN Jiao & CUI HengJian Department of Statistics and Financial Mathematics, School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems (Beijing Normal University), Ministry of Education, Beijing 100875, China | 2010 | Science China Mathematics2010，53，2： | 4 |
| 5 | EMPIRICAL LIKELIHOOD CONFIDENCE REGION FOR PARAMETERS IN LINEAR ERRORS-IN-VARIABLES MODELS WITH MISSING DATA显示文摘multivariate 线性 errors-in-variables 模型 regressors 什么时候在在 Rubin (1976 ) 的意义的随机是失踪的,在这份报纸被考虑。为 0 在这建模的一个参数的一个抑制实验可能性的信心区域被建议,它被基于反的概率把相应于加权的摆平的直角的距离的 20 个函数与 0 的一个抑制区域相结合构造。在真参数的实验木头可能性的比率收敛到标准 chi 平方分发,这被显示出。模拟证明建议信心区域的范围率接近名字的水平,信心间隔的长度是比反的概率的正常近似的那些狭窄的在大多数情况中的加权的调整最不方形的评估者。一个真实例子被学习,结果支持理论和模拟结论。 | Juan ZHANG Hengjian CUI | 2011 | Journal of Systems Science & Complexity2011，24，3： | 3 |
| 6 | DISCRIMINANT ANALYSIS BASED ON STATISTICAL DEPTH显示文摘In the past two decades,many statistical depth functions seemed as powerful exploratoryand inferential tools for multivariate data analysis have been presented.In this paper,a new depthfunction family that meets four properties mentioned in Zuo and Serfling(2000)is proposed.Then aclassification rule based on the depth function family is proposed.The classification parameter b couldbe modified according to the type-Ⅰ error α,and the estimator of b has the consistency and achievesthe convergence rate n^(-1/2).With the help of the proper selection for depth family parameter c,theapproach for discriminant analysis could minimize the type-Ⅱ error β.A simulation study and a realdata example compare the performance of the different discriminant methods. | Jiao JIN·Hengjian CUI School of Mathematical Sciences,Key Laboratory of Mathematics and Complex Systems,Ministry of Education, Beijing Normal University,Beijing 100875,China. | 2010 | Journal of Systems Science & Complexity2010，23，2： | 3 |
| 7 | Consistency and normality of Huber-Dutter estimators for partial linear model显示文摘For partial linear model Y = Xτβ0 + g0(T) + with unknown β0 ∈ Rd and an unknown smooth function g0, this paper considers the Huber-Dutter estimators of β0, scale σ for the errors and the function g0 approximated by the smoothing B-spline functions, respectively. Under some regularity conditions, the Huber-Dutter estimators of β0 and σ are shown to be asymptotically normal with the rate of convergence n-1/2 and the B-spline Huber-Dutter estimator of g0 achieves the optimal rate of convergence in nonparametric regression. A simulation study and two examples demonstrate that the Huber-Dutter estimator of β0 is competitive with its M-estimator without scale parameter and the ordinary least square estimator. | TONG XingWei CUI HengJian YU Peng | 2008 | Science China Mathematics2008，51，10： | 3 |
| 8 | Sieve M-estimator for a semi-functional linear model显示文摘We propose sieve M-estimator for a semi-functional linear model in which the scalar response is explained by a linear operator of functional predictor and smooth functions of some real-valued random variables.Spline estimators of the functional coefficient and the smooth functions are considered,and by selecting appropriate knot numbers the optimal convergence rate and the asymptotic normality can be obtained under some mild conditions.Some simulation results and a real data example are presented to illustrate the performance of our estimation method. | HUANG LeLe WANG HuiWen CUI HengJian WANG SiYang | 2015 | Science China Mathematics2015，58，11： | 2 |
| 9 | Empirical likelihood inference for semi-parametric estimating equations显示文摘Qin and Lawless (1994) established the statistical inference theory for the empirical likelihood of the general estimating equations. However, in many practical problems, some unknown functional parts h(t) appear in the corresponding estimating equations EFG(X, h(T), β) = 0. In this paper, the empirical likelihood inference of combining information about unknown parameters and distribution function through the semiparametric estimating equations are developed, and the corresponding Wilk's theorem is established. The simulations of several useful models are conducted to compare the finite-sample performance of the proposed method and that of the normal approximation based method. An illustrated real example is also presented. | WANG ShanShan CUI HengJian LI RunZe | 2013 | Science China Mathematics2013，56，6： | 1 |
| 10 | Sieve M-estimation for semiparametric varying-coefficient partially linear regression model显示文摘This article considers a semiparametric varying-coefficient partially linear regression model.The semiparametric varying-coefficient partially linear regression model which is a generalization of the partially linear regression model and varying-coefficient regression model that allows one to explore the possibly nonlinear effect of a certain covariate on the response variable.A sieve M-estimation method is proposed and the asymptotic properties of the proposed estimators are discussed.Our main object is to estimate the nonparametric component and the unknown parameters simultaneously.It is easier to compute and the required computation burden is much less than the existing two-stage estimation method.Furthermore,the sieve M-estimation is robust in the presence of outliers if we choose appropriate ρ(·).Under some mild conditions,the estimators are shown to be strongly consistent;the convergence rate of the estimator for the unknown nonparametric component is obtained and the estimator for the unknown parameter is shown to be asymptotically normally distributed.Numerical experiments are carried out to investigate the performance of the proposed method. | HU Tao 1,2 & CUI HengJian 1,2 1 School of Mathematical Sciences,Beijing Normal University,Laboratory of Mathematics and Complex Systems,Ministry of Education,Beijing 100875,China 2 School of Mathematical Sciences,Capital Normal University,Beijing 100048,China | 2010 | Science China Mathematics2010，53，8： | 1 |
| 11 | Generalized F-Test for High Dimensional Regression Coefficients of Partially Linear Models显示文摘This paper proposes a test procedure for testing the regression coefficients in high dimensional partially linear models based on the F-statistic. In the partially linear model, the authors first estimate the unknown nonlinear component by some nonparametric methods and then generalize the F-statistic to test the regression coefficients under some regular conditions. During this procedure, the estimation of the nonlinear component brings much challenge to explore the properties of generalized F-test. The authors obtain some asymptotic properties of the generalized F-test in more general cases,including the asymptotic normality and the power of this test with p/n ∈(0, 1) without normality assumption. The asymptotic result is general and by adding some constraint conditions we can obtain the similar conclusions in high dimensional linear models. Through simulation studies, the authors demonstrate good finite-sample performance of the proposed test in comparison with the theoretical results. The practical utility of our method is illustrated by a real data example. | WANG Siyang CUI Hengjian | 2017 | Journal of Systems Science & Complexity2017，30，5： | 1 |
| 12 | On parameter estimation for semi-linear errors-in-variables models 显示文摘 | Cui Hengjian Li Rongcai | 1998 | J of Multivariate Analysis1998，64，： | 1 |
| 13 | Asymptotic properties of gGeneralized MAD estimators in EV model 显示文摘 | Cui Hengjian | 1997 | Science in China:Series A1997，27，2： | 1 |
| 14 | Empirical likelihood confidence region for parameter in the errors-in-variables models 显示文摘 | Cui Hengjian Chen Songxi | 2003 | J Multivariate Anal2003，84，1： | 1 |
| 15 | Empirical likelihood confidence region for parameter in the errors- in-variables models 显示文摘 | Cui Hengjian Chen Songxi | 2003 | J Multivariate Anal2003，84，1： | 1 |
| 16 | Empirical likelihood ratio confidence regions in EV model 显示文摘 | Gao Xiuhong Cui Hengjian | 2001 | J of BJ Nor Univ:Nat Sci2001，37，5： | 1 |
| 17 | Robust U-type test for high dimensional regression coefficients using refitted cross-validation variance estimation显示文摘This paper aims to develop a new robust U-type test for high dimensional regression coefficients using the estimated U-statistic of order two and refitted cross-validation error variance estimation. It is proved that the limiting null distribution of the proposed new test is normal under two kinds of ordinary models.We further study the local power of the proposed test and compare with other competitive tests for high dimensional data. The idea of refitted cross-validation approach is utilized to reduce the bias of sample variance in the estimation of the test statistic. Our theoretical results indicate that the proposed test can have even more substantial power gain than the test by Zhong and Chen(2011) when testing a hypothesis with outlying observations and heavy tailed distributions. We assess the finite-sample performance of the proposed test by examining its size and power via Monte Carlo studies. We also illustrate the application of the proposed test by an empirical analysis of a real data example. | GUO WenWen CHEN YongShuai CUI HengJian | 2016 | Science China Mathematics2016，59，12： | 1 |
| 18 | On the Stahel-Do- noho Estimator and Depth-weighted Means of Multivariate Data 显示文摘 | Yijun Zuo Hengjian Cui Xuming He | 2004 | The Annals of Statistics2004，32，1： | 1 |
| 19 | On regression estimators with de -nosied variables显示文摘 | Cui Hengjian He Xuming Zhu Lixing | 2002 | Statistica Sinica2002，12，： | 1 |
| 20 | Empirical likelihood confidence regions for parameters in error-in-variables models 显示文摘 | | 2002 | Journal of Multivariate Analysis2002，84，1： | 1 |
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