| Reducing component estimation for varying coefficient models with longitudinal data |
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| 作者单位： | 1，2 |
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| 摘 要： | Varying-coefficient models with longitudinal observations are very useful in epidemiology and some other practical fields.In 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- dependent.The asymptotic properties of the estimators,such as consistency,rate of convergence and asymptotic distribution,are derived.The 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 smoothness.Finite sample properties of our procedures are studied through Monte Carlo simulations.
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| 收稿时间： | 16 February 2005 |
| 修稿时间： | 19 June 2007 |
Reducing component estimation for varying coefficient models with longitudinal data |
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| Authors: | Tang QingGuo and Wang JinDe |
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| Institution: | (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 |
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| Abstract: | Varying-coefficient models with longitudinal observations are very useful in epidemiology and some other practical fields.In 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- dependent.The asymptotic properties of the estimators,such as consistency,rate of convergence and asymptotic distribution,are derived.The 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 smoothness.Finite sample properties of our procedures are studied through Monte Carlo simulations. |
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| Keywords: | varying coefficient model longitudinal data nonparametric estimation reducing component estimators asymptotic normality |
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