ESTIMATION FOR A PARTIAL-LINEAR SINGLE-INDEX MODEL
ESTIMATION FOR A PARTIAL-LINEAR SINGLE-INDEX MODEL
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DOI：
10.1214/09-aos712
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发表时间：
2010-02-01
影响因子：
4.5
通讯作者：
Chong, Yun Sam
中科院分区：
文献类型：
--
作者：
Wang, Jane-Ling;Xue, Liugen;Chong, Yun Sam
本文研究了偏线性单指标模型的估计问题。提出了一种两阶段估计方法，用于估计单个指标的链接函数和单个指标中的参数，以及模型的线性分量中的参数。两个参数分量都建立了渐进正态性。对于指数，一个约束估计方程导致一个渐近更有效的估计比现有的估计在这个意义上，它是一个较小的极限方差。非参数连接函数的估计达到最优收敛速度，并得到结构误差方差。此外，这些结果有助于构造置信区域和未知参数的假设检验。进行了模拟研究，并说明了应用程序到一个真实的数据集。扩展到多个指数简要概述。
In this paper, we study the estimation for a partial-linear single-index model. A two-stage estimation procedure is proposed to estimate the link function for the single index and the parameters in the single index, as well as the parameters in the linear component of the model. Asymptotic normality is established for both parametric components. For the index, a constrained estimating equation leads to an asymptotically more efficient estimator than existing estimators in the sense that it is of a smaller limiting variance. The estimator of the nonparametric link function achieves optimal convergence rates, and the structural error variance is obtained. In addition, the results facilitate the construction of confidence regions and hypothesis testing for the unknown parameters. A simulation study is performed and an application to a real dataset is illustrated. The extension to multiple indices is briefly sketched.