Multivariate prediction using softly shrunk reduced-rank regression
Multivariate prediction using softly shrunk reduced-rank regression
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DOI：
10.2307/2685607
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发表时间：
2000-02-01
影响因子：
1.8
通讯作者：
Aldrin, M
中科院分区：
文献类型：
--
作者：
Aldrin, M
多元回归被认为是重点预测。当训练数据中的观测值与要估计的参数数量相比很少时，普通最小二乘法往往会产生不稳定的估计值，从而产生不确定的预测。因此，需要在这种情况下工作良好的方法。本文提出了一种新的基于降秩回归的替代预测方法。降秩回归的方法使用回归系数矩阵的普通最小二乘估计的某种分解，并将该分解的最后一项精确地缩小到0。我提出了一种新的方法与软收缩的条款在分解。此外，降秩回归，以及新的软收缩降秩回归，与主成分回归相结合。对这些方法进行了修改，以处理响应变量中的缺失观测值。各种方法进行了比较，通过仿真研究。软收缩降秩回归，可能与主成分相结合，被证明是最好的整体方法，并且在观测值很少的情况下，普通最小二乘法的改进特别大。
Multivariate regression is considered with emphasis on prediction. Ordinary least squares tends to yield unstable estimates and consequently uncertain predictions when there are few observations in the training data compared to the number of parameters to be estimated. Thus, there is a need for methods that work well in such situations. This article presents a new alternative prediction method based on reduced-rank regression. The method of reduced-rank regression uses a certain decomposition of the ordinary least squares estimate of the matrix of regression coefficients, and shrinks the last terms of this decomposition exactly to 0. I suggest a new method with soft shrinkage of the terms in the decomposition. Furthermore, the reduced-rank regression, as well as the new softly shrunk reduced-rank regression, are combined with principal components regression. The methods are modified to handle missing observations in the response variables. The various methods are compared through a simulation study. Softly shrunk reduced-rank regression, possibly combined with principal components, turns out to be the best overall method, and the improvement over ordinary least squares is particularly large in situations with few observations.