论文标题
非参数通用线性模型的强大而有效的估计
Robust and efficient estimation of nonparametric generalized linear models
论文作者
论文摘要
通用线性模型是用于分析不同数据集的灵活工具，但是经典配方要求正确指定参数组件，并且数据不包含非典型观察结果。为了解决这些缺点，我们介绍并研究了一个非参数全等级和较低排名样条估计器的家庭，这是由于惩罚能力差异最小化所致。拟议的估计器类别可容易实施，可为外围观察提供高度保护，并可以根据清洁数据的任意高效率进行调整。我们表明，在弱假设下，这些估计器以快速的速度收敛，并在模拟研究和两个真实数据示例中说明了它们高度竞争性的表现。
Generalized linear models are flexible tools for the analysis of diverse datasets, but the classical formulation requires that the parametric component is correctly specified and the data contain no atypical observations. To address these shortcomings we introduce and study a family of nonparametric full rank and lower rank spline estimators that result from the minimization of a penalized power divergence. The proposed class of estimators is easily implementable, offers high protection against outlying observations and can be tuned for arbitrarily high efficiency in the case of clean data. We show that under weak assumptions these estimators converge at a fast rate and illustrate their highly competitive performance on a simulation study and two real-data examples.
