Wang Li, Liu Xiang, Liang Hua, Carroll Raymond J
Department of Statistics, University of Georgia, Athens, Georgia 30602, USA,
Ann Stat. 2011;39(4):1827-1851. doi: 10.1214/11-AOS885SUPP.
We study generalized additive partial linear models, proposing the use of polynomial spline smoothing for estimation of nonparametric functions, and deriving quasi-likelihood based estimators for the linear parameters. We establish asymptotic normality for the estimators of the parametric components. The procedure avoids solving large systems of equations as in kernel-based procedures and thus results in gains in computational simplicity. We further develop a class of variable selection procedures for the linear parameters by employing a nonconcave penalized quasi-likelihood, which is shown to have an asymptotic oracle property. Monte Carlo simulations and an empirical example are presented for illustration.
我们研究广义相加部分线性模型,提出使用多项式样条平滑来估计非参数函数,并推导基于拟似然的线性参数估计量。我们建立了参数分量估计量的渐近正态性。该方法避免了像基于核的方法那样求解大型方程组,从而在计算简便性方面有所收获。我们通过采用非凹惩罚拟似然进一步开发了一类线性参数的变量选择程序,该程序被证明具有渐近似然估计性质。给出了蒙特卡罗模拟和一个实证例子进行说明。