ESTIMATION AND TESTING FOR PARTIALLY LINEAR SINGLE-INDEX MODELS.
ESTIMATION AND TESTING FOR PARTIALLY LINEAR SINGLE-INDEX MODELS.
复制标题
部分线性单指数模型的估计和测试。
DOI：
10.1214/10-aos835
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发表时间：
2010-12-01
影响因子：
4.5
通讯作者：
Tsai CL
中科院分区：
文献类型：
--
作者：
Liang H;Liu X;Li R;Tsai CL
在部分线性单指标模型中，得到了回归系数的半参数有效轮廓最小二乘估计。我们还采用平滑剪切绝对偏差惩罚（SCAD）的方法，同时选择变量和估计回归系数。我们证明了所得的SCAD估计是相容的，并具有预言性质。随后，我们证明了一个建议的调整参数选择器，BIC，确定真正的模型一致。最后，我们分别对参数系数和非参数分量进行了线性假设检验和拟合优度检验。蒙特卡洛研究也被提出。
In partially linear single-index models, we obtain the semiparametrically efficient profile least-squares estimators of regression coefficients. We also employ the smoothly clipped absolute deviation penalty (SCAD) approach to simultaneously select variables and estimate regression coefficients. We show that the resulting SCAD estimators are consistent and possess the oracle property. Subsequently, we demonstrate that a proposed tuning parameter selector, BIC, identifies the true model consistently. Finally, we develop a linear hypothesis test for the parametric coefficients and a goodness-of-fit test for the nonparametric component, respectively. Monte Carlo studies are also presented.