Local likelihood estimation in generalized additive models
Local likelihood estimation in generalized additive models
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DOI：
10.1111/1467-9469.00333
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发表时间：
2003-06-01
影响因子：
1
通讯作者：
Opsomer, JD
中科院分区：
文献类型：
--
作者：
Kauermann, G;Opsomer, JD
广义加性模型是一类流行的多元非参数回归模型，在很大程度上是由于易于使用的局部评分估计算法。然而，局部评分估计量的理论性质知之甚少。在本文中，我们提出了广义加性模型的局部似然估计量，该估计量与局部多项式回归拟合的局部评分估计量密切相关。我们推导出的估计的统计性质，并表明，它实现了相同的渐近收敛速度作为一个一维的局部多项式回归估计。我们还提出了一个野生自助估计计算逐点的置信区间的添加剂成分函数。所提出的估计的实际行为是通过模拟实验说明。
Generalized additive models are a popular class of multivariate non-parametric regression models, due in large part to the ease of use of the local scoring estimation algorithm. However, the theoretical properties of the local scoring estimator are, poorly understood. In this article, we propose a local likelihood estimator for generalized additive models that is closely related to the local scoring estimator fitted by local polynomial regression. We derive the statistical properties of the estimator and show that it achieves the same asymptotic convergence rate as a one-dimensional local polynomial regression estimator. We also propose a wild bootstrap estimator for calculating point-wise confidence intervals for the additive component functions. The practical behaviour of the proposed estimator is illustrated through a simulation experiment.