Constrained penalized splines
Constrained penalized splines
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DOI：
10.1002/cjs.10137
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发表时间：
2012-03-01
影响因子：
0.6
通讯作者：
Meyer, Mary C.
中科院分区：
文献类型：
--
作者：
Meyer, Mary C.
当光滑性假设成立时，惩罚样条是一种常用的函数估计方法。本文提出了在单调性或凸性等附加形状约束下使用惩罚样条进行估计和推理的方法。约束惩罚样条估计具有相同的收敛速度，相应的无约束惩罚样条，虽然在实践中的平方误差损失通常是较小的约束版本。惩罚参数可以用广义交叉验证来选择，这也提供了一种用于确定形状限制是否成立的方法。该方法不是一个正式的假设检验，但被证明有很好的大样本特性，模拟表明，它与现有的单调性测试比较。给出了部分线性模型、广义回归模型和变系数模型的推广，并举例说明了方法的实用性。The Canadian Journal of Statistics 40：190206; 2012（C）2012加拿大统计学会
The penalized spline is a popular method for function estimation when the assumption of smoothness is valid. In this paper, methods for estimation and inference are proposed using penalized splines under additional constraints of shape, such as monotonicity or convexity. The constrained penalized spline estimator is shown to have the same convergence rates as the corresponding unconstrained penalized spline, although in practice the squared error loss is typically smaller for the constrained versions. The penalty parameter may be chosen with generalized cross-validation, which also provides a method for determining if the shape restrictions hold. The method is not a formal hypothesis test, but is shown to have nice large-sample properties, and simulations show that it compares well with existing tests for monotonicity. Extensions to the partial linear model, the generalized regression model, and the varying coefficient model are given, and examples demonstrate the utility of the methods. The Canadian Journal of Statistics 40: 190206; 2012 (C) 2012 Statistical Society of Canada