部分非线性混合效应模型在纵向数据下的估计
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摘要
考虑纵向数据下的部分非线性混合效应模型。利用样条和广义最小二乘方法构造非参数函数的g(·)估计,同时利用Gauss-Newton法构造未知参数β的估计。在一定条件下构造了模型中方差分量的估计,并证实前述估计量的渐近正态性和相合性。通过数值模拟和实例分析证实了该研究方法的优良性和有效性。
In this article a partially nonlinear random effect model for longitudinal data is proposed. To estimate the smooth function g(.), this paper introduces B-spline and generalizes least squares. It also uses Gauss-Newton method to estimate the parameter β. Finally, the paper considers the estimation for the variance components, and proves the consistency and the asymptotic normality of the estimators. Simulation and real examples show that our algorithm is stable numerically and performs well.
In this article a partially nonlinear random effect model for longitudinal data is proposed. To estimate the smooth function g(.), this paper introduces B-spline and generalizes least squares. It also uses Gauss-Newton method to estimate the parameter β. Finally, the paper considers the estimation for the variance components, and proves the consistency and the asymptotic normality of the estimators. Simulation and real examples show that our algorithm is stable numerically and performs well.
引文
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[5]符利勇,张会儒,李春明,等.非线性混合效应模型参数估计方法分析[J].林业科学,2013,49(1):114-119.
[6]LIANG H,WU H L,CARROLL R J.The relationship between virologic and immunologic responses in AIDSclinical research using mixed-effects varying-coefficient models with measurement error[J].Biostatistics,2003(4):297-312.
[7]BAI Y,FUNG W K,ZHU Z Y.Penalized quadratic inference functions for single-index models with longitudinal data[J].Journal of Multivariate Analysis,2009,100(1):152-161.
[8]HUANG J Z,WU C O,ZHOU L.Polynomial spline estimation and inference for varying coefficient models with longitudinaldata[J].StatisticaSinica,2004,14(3):763-788.
[9]LI R,NIE L.Efficient statistical inference procedures for partially nonlinear models and their applications[J].Biometrics,2008(64):904-911.
[2]PANG Z,XUE L G.Estimation for the single-index models with random effects[J].Computational Statistics and Data Analysis,2012,56(6):1837-1853.
[3]LI W B,XUE L G.Efficient inference about the partially linear varying coefficient model with random effect for longitudinal data[J].Springer Berlin Heidelberg,2013(391):573-583.
[4]LI W B,XUE L G.Efficient inference in a generalized partially linear model with random effect for longitudinal data[J].Communication in Statistics-Theory and Methods,2015,44(2):241-260.
[5]符利勇,张会儒,李春明,等.非线性混合效应模型参数估计方法分析[J].林业科学,2013,49(1):114-119.
[6]LIANG H,WU H L,CARROLL R J.The relationship between virologic and immunologic responses in AIDSclinical research using mixed-effects varying-coefficient models with measurement error[J].Biostatistics,2003(4):297-312.
[7]BAI Y,FUNG W K,ZHU Z Y.Penalized quadratic inference functions for single-index models with longitudinal data[J].Journal of Multivariate Analysis,2009,100(1):152-161.
[8]HUANG J Z,WU C O,ZHOU L.Polynomial spline estimation and inference for varying coefficient models with longitudinaldata[J].StatisticaSinica,2004,14(3):763-788.
[9]LI R,NIE L.Efficient statistical inference procedures for partially nonlinear models and their applications[J].Biometrics,2008(64):904-911.