Scaled Predictor Envelopes and Partial Least-Squares Regression
Scaled Predictor Envelopes and Partial Least-Squares Regression
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DOI：
10.1080/00401706.2015.1017611
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发表时间：
2016-05-01
期刊：
影响因子：
2.5
通讯作者：
Su, Zhihua
中科院分区：
文献类型：
--
作者：
Cook, R. Dennis;Su, Zhihua
偏最小二乘(偏最小二乘)是应用统计学中广泛使用的预测方法，特别是在化学计量学的应用中。然而，在预测因子的尺度变换下，偏最小二乘不是不变的或等变的，这往往将其范围限制在预测因子以相同或相似的单位测量的回归中。Cook、Helland和Su(2013)在新兴的包络方法和偏最小二乘法之间建立了联系，允许在传统的基于可能性的框架中处理偏最小二乘法。在这篇文章中，我们利用偏最小二乘与包络之间的联系来发展一种新的方法--比例预测包络(SPE)--将预测比例结合到偏最小二乘类型的应用中。通过估计适当的尺度，SPE估计器可以提供比偏最小二乘法更高的效率收益，并进一步减少预测误差。文中给出了仿真和算例，验证了理论的正确性。
Partial least squares (PLS) is a widely used method for prediction in applied statistics, especially in chemometrics applications. However, PLS is not invariant or equivariant under scale transformations of the predictors, which tends to limit its scope to regressions in which the predictors are measured in the same or similar units. Cook, Helland, and Su (2013) built a connection between nascent envelope methodology and PLS, allowing PLS to be addressed in a traditional likelihood-based framework. In this article, we use the connection between PLS and envelopes to develop a new method-scaled predictor envelopes (SPE)-that incorporates predictor scaling into PLS-type applications. By estimating the appropriate scales, the SPE estimators can offer efficiency gains beyond those given by PLS, and further reduce prediction errors. Simulations and an example are given to support the theoretical claims.