相关性数据下变系数模型的非参数估计
|
摘要
文章研究了相关性数据下变系数模型的非参数估计问题。利用多项式样条回归方法对未知函数系数进行基函数近似,构造关于基函数系数的惩罚修正二次推断函数,得到基函数系数的估计,建立了估计的渐近性质,并通过割线法得到了估计的数值解。结果表明,估计方法具有良好的实际应用价值。
This paper studies the nonparametric estimation of variable coefficient models with correlation data. By using polynomial spline regression method to approximate the unknown function coefficients, the paper constructs a penalty correction quadratic inference function about the coefficient of basis function, and gets an estimate of the coefficient of basis function to establish the asymptotic property of the estimator. As a result, the estimated numerical solution is obtained by using secant method. Results show that the proposed estimation method has good practical application value.
This paper studies the nonparametric estimation of variable coefficient models with correlation data. By using polynomial spline regression method to approximate the unknown function coefficients, the paper constructs a penalty correction quadratic inference function about the coefficient of basis function, and gets an estimate of the coefficient of basis function to establish the asymptotic property of the estimator. As a result, the estimated numerical solution is obtained by using secant method. Results show that the proposed estimation method has good practical application value.
引文
[1]Song P X. Correlated Data Analysis[M]. New York:Springer, 2007.
[2]赵明涛,何晓群.纵向数据非参数模型的二次推断函数估计[J].统计与决策, 2013,(7).
[3]Hedeker D, Gibbons D. Longitudinal Data Analysis[M]. New Jersey:John Willey&Sons,2006.
[4]Lee Y, Nelder, J A. Longitudinal Data Analysis Using Generalized Linear Models[J]. Biometrika, 1986, 73(1).
[5]Lee Y, Nelder J A. Hierarchical Generalized Linear Models(With Dis?cussion)[J]. Journel of Roal Statistical Society, Ser B, 1996, 58(4).
[6]Crowder M. On the Use of a Working Correlation Matrix in Using Gen?eralized Linear Models for Repeated Measures[J]. Biometrika, 1995,82(2).
[7]Qu A, Lindsay B G, Li B. Improving Generalized Estimating Equations Using Quadratic Inference Functions[J]. Biometrika,2000, 87(4).
[8]Qu A, Li R. Quadratic Inference Functions for Varying Coefficient Models with Longitudinal Data[J]. Biometrics, 2006, 62(2).
[9]Song P X, Jiang Z C, Park E, et al. Quadratic Inference Functions in Marginal Models for Longitudinal Data[J]. Statistics in Medicine.2009, 28(29).
[10]Qu A, Song P X. Assessing Robustness of Generalized Estimating Equations and Quadratic Inference Functions[J]. Biometrika, 2004,91(2).
[11]Hansen L. Large Sample Properties of Generalized Method of Mo?ments Estimators[J]. Econometrica, 1982, 50(4).
[12]Westgate P M, Braun T M. An Improved Quadratic Inference Func?tion for Parameter Estimation in the Analysis of Correlated Data[J].Stat Med,2013, 32(19).
[13]Tian R, Xue L, Xu D. Automatic Variable Selection for Varying Coef?ficient Models With Longitudinal Data[J]. Statistics&Probability Letters, 2016, 119(12).
[14]Khan M N, Heenaye M. A Computationally Efficient Algorithm to Solve Generalized Method of Moments Estimating Equations Based on Secant-vector Divisions Procedure[J]. International Journal of Scientific and Statistical Computing,2011, 2(1).
[2]赵明涛,何晓群.纵向数据非参数模型的二次推断函数估计[J].统计与决策, 2013,(7).
[3]Hedeker D, Gibbons D. Longitudinal Data Analysis[M]. New Jersey:John Willey&Sons,2006.
[4]Lee Y, Nelder, J A. Longitudinal Data Analysis Using Generalized Linear Models[J]. Biometrika, 1986, 73(1).
[5]Lee Y, Nelder J A. Hierarchical Generalized Linear Models(With Dis?cussion)[J]. Journel of Roal Statistical Society, Ser B, 1996, 58(4).
[6]Crowder M. On the Use of a Working Correlation Matrix in Using Gen?eralized Linear Models for Repeated Measures[J]. Biometrika, 1995,82(2).
[7]Qu A, Lindsay B G, Li B. Improving Generalized Estimating Equations Using Quadratic Inference Functions[J]. Biometrika,2000, 87(4).
[8]Qu A, Li R. Quadratic Inference Functions for Varying Coefficient Models with Longitudinal Data[J]. Biometrics, 2006, 62(2).
[9]Song P X, Jiang Z C, Park E, et al. Quadratic Inference Functions in Marginal Models for Longitudinal Data[J]. Statistics in Medicine.2009, 28(29).
[10]Qu A, Song P X. Assessing Robustness of Generalized Estimating Equations and Quadratic Inference Functions[J]. Biometrika, 2004,91(2).
[11]Hansen L. Large Sample Properties of Generalized Method of Mo?ments Estimators[J]. Econometrica, 1982, 50(4).
[12]Westgate P M, Braun T M. An Improved Quadratic Inference Func?tion for Parameter Estimation in the Analysis of Correlated Data[J].Stat Med,2013, 32(19).
[13]Tian R, Xue L, Xu D. Automatic Variable Selection for Varying Coef?ficient Models With Longitudinal Data[J]. Statistics&Probability Letters, 2016, 119(12).
[14]Khan M N, Heenaye M. A Computationally Efficient Algorithm to Solve Generalized Method of Moments Estimating Equations Based on Secant-vector Divisions Procedure[J]. International Journal of Scientific and Statistical Computing,2011, 2(1).