Functional projection pursuit regression
Functional projection pursuit regression
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DOI：
10.1007/s11749-012-0306-2
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发表时间：
2013-06
期刊：
影响因子：
1.3
通讯作者：
F. Ferraty;A. Goia;E. Salinelli;P. Vieu
中科院分区：
文献类型：
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作者：
F. Ferraty;A. Goia;E. Salinelli;P. Vieu
在本文中，我们介绍了一种灵活的方法来近似的回归函数的情况下，功能预测和标量响应。根据投影寻踪回归原理，我们推导出一种加性分解，它利用预测变量最有趣的投影来解释响应。一方面，这种方法可以避免众所周知的维数灾难问题，另一方面，它可以作为一种探索性的工具，用于分析功能数据集。这种分解的条款估计与样条近似和一维Nadaraya-Watson方法相结合的程序。从理论和实践的角度说明了我们的程序的良好行为。渐近结果表明，在添加剂分解中的条款可以估计，而不会遭受的维数问题，而一些应用程序的真实的和模拟数据显示我们的方法的高预测性能。
In this paper we introduce a flexible approach to approximate the regression function in the case of a functional predictor and a scalar response. Following the Projection Pursuit Regression principle, we derive an additive decomposition which exploits the most interesting projections of the prediction variable to explain the response. On one hand, this approach allows us to avoid the well-known curse of dimensionality problem, and, on the other one, it can be used as an exploratory tool for the analysis of functional dataset. The terms of such decomposition are estimated with a procedure that combines a spline approximation and the one-dimensional Nadaraya–Watson approach. The good behavior of our procedure is illustrated from theoretical and practical points of view. Asymptotic results state that the terms in the additive decomposition can be estimated without suffering from the dimensionality problem, while some applications to real and simulated data show the high predictive performance of our method.