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B-spline estimation for varying coefficient regression with spatial data 被引量:3
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作者 TANG QingGuo CHENG LongSheng 《Science China Mathematics》 SCIE 2009年第11期2321-2340,共20页
This paper considers a nonparametric varying coefficient regression with spatial data. A global smoothing procedure is developed by using B-spline function approximations for estimating the coefficient functions. Unde... This paper considers a nonparametric varying coefficient regression with spatial data. A global smoothing procedure is developed by using B-spline function approximations for estimating the coefficient functions. Under mild regularity assumptions,the global convergence rates of the B-spline estimators of the unknown coefficient functions are established. Asymptotic results show that our B-spline estimators achieve the optimal convergence rate. The asymptotic distributions of the B-spline estimators of the unknown coefficient functions are also derived. A procedure for selecting smoothing parameters is given. Finite sample properties of our procedures are studied through Monte Carlo simulations. Application of the proposed method is demonstrated by examining voting behaviors across US counties in the 1980 presidential election. 展开更多
关键词 spatial data varying coefficient regression B-spline estimators convergence rate asymptotic distribution 62G05 62g08
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Local asymptotic behavior of regression splines for marginal semiparametric models with longitudinal data 被引量:2
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作者 QIN GuoYou ZHU ZhongYi 《Science China Mathematics》 SCIE 2009年第9期1982-1994,共13页
In this paper, we study the local asymptotic behavior of the regression spline estimator in the framework of marginal semiparametric model. Similarly to Zhu, Fung and He (2008), we give explicit expression for the asy... In this paper, we study the local asymptotic behavior of the regression spline estimator in the framework of marginal semiparametric model. Similarly to Zhu, Fung and He (2008), we give explicit expression for the asymptotic bias of regression spline estimator for nonparametric function f. Our results also show that the asymptotic bias of the regression spline estimator does not depend on the working covariance matrix, which distinguishes the regression splines from the smoothing splines and the seemingly unrelated kernel. To understand the local bias result of the regression spline estimator, we show that the regression spline estimator can be obtained iteratively by applying the standard weighted least squares regression spline estimator to pseudo-observations. At each iteration, the bias of the estimator is unchanged and only the variance is updated. 展开更多
关键词 asymptotic bias B-SPLINE generalized estimating equation longitudinal data semiparametric models 62F35 62g08
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Two-stage local M-estimation of additive models 被引量:1
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作者 JIANG JianCheng LI JianTao 《Science China Mathematics》 SCIE 2008年第7期1315-1338,共24页
This paper studies local M-estimation of the nonparametric components of additive models. A two-stage local M-estimation procedure is proposed for estimating the additive components and their derivatives. Under very m... This paper studies local M-estimation of the nonparametric components of additive models. A two-stage local M-estimation procedure is proposed for estimating the additive components and their derivatives. Under very mild conditions, the proposed estimators of each additive component and its derivative are jointly asymptotically normal and share the same asymptotic distributions as they would be if the other components were known. The established asymptotic results also hold for two particular local M-estimations: the local least squares and least absolute deviation estimations. However, for general two-stage local M-estimation with continuous and nonlinear ψ-functions, its implementation is time-consuming. To reduce the computational burden, one-step approximations to the two-stage local M-estimators are developed. The one-step estimators are shown to achieve the same efficiency as the fully iterative two-stage local M-estimators, which makes the two-stage local M-estimation more feasible in practice. The proposed estimators inherit the advantages and at the same time overcome the disadvantages of the local least-squares based smoothers. In addition, the practical implementation of the proposed estimation is considered in details. Simulations demonstrate the merits of the two-stage local M-estimation, and a real example illustrates the performance of the methodology. 展开更多
关键词 local M-estimation one-step approximation orthogonal series estimator TWO-STAGE 62G35 62G05 62g08
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Consistency and asymptotic normality of profilekernel and backfitting estimators in semiparametric reproductive dispersion nonlinear models
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作者 TANG NianSheng CHEN XueDong WANG XueRen 《Science China Mathematics》 SCIE 2009年第4期757-770,共14页
Semiparametric reproductive dispersion nonlinear model (SRDNM) is an extension of nonlinear reproductive dispersion models and semiparametric nonlinear regression models, and includes semiparametric nonlinear model an... Semiparametric reproductive dispersion nonlinear model (SRDNM) is an extension of nonlinear reproductive dispersion models and semiparametric nonlinear regression models, and includes semiparametric nonlinear model and semiparametric generalized linear model as its special cases. Based on the local kernel estimate of nonparametric component, profile-kernel and backfitting estimators of parameters of interest are proposed in SRDNM, and theoretical comparison of both estimators is also investigated in this paper. Under some regularity conditions, strong consistency and asymptotic normality of two estimators are proved. It is shown that the backfitting method produces a larger asymptotic variance than that for the profile-kernel method. A simulation study and a real example are used to illustrate the proposed methodologies. 展开更多
关键词 asymptotic normality backfitting method consistency profile-kernel method semiparametric reproductive dispersion nonlinear models 62G05 62g08 62G20
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Dimension reduction based on weighted variance estimate
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作者 ZHAO JunLong1 & XU XingZhong2 1 Department of Mathematics, Beihang University Laboratory of Mathematics, Information and Behavior of the Ministry of Education, Beijing 100083, China 2 Department of Mathematics, Beijing Institute of Technology, Beijing 100081, China 《Science China Mathematics》 SCIE 2009年第3期539-560,共22页
In this paper, we propose a new estimate for dimension reduction, called the weighted variance estimate (WVE), which includes Sliced Average Variance Estimate (SAVE) as a special case. Bootstrap method is used to sele... In this paper, we propose a new estimate for dimension reduction, called the weighted variance estimate (WVE), which includes Sliced Average Variance Estimate (SAVE) as a special case. Bootstrap method is used to select the best estimate from the WVE and to estimate the structure dimension. And this selected best estimate usually performs better than the existing methods such as Sliced Inverse Regression (SIR), SAVE, etc. Many methods such as SIR, SAVE, etc. usually put the same weight on each observation to estimate central subspace (CS). By introducing a weight function, WVE puts different weights on different observations according to distance of observations from CS. The weight function makes WVE have very good performance in general and complicated situations, for example, the distribution of regressor deviating severely from elliptical distribution which is the base of many methods, such as SIR, etc. And compared with many existing methods, WVE is insensitive to the distribution of the regressor. The consistency of the WVE is established. Simulations to compare the performances of WVE with other existing methods confirm the advantage of WVE. 展开更多
关键词 central subspace contour regression sliced average variance estimate sliced inverse regression sufficient dimension reduction weight function 62g08 62H05
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