标题： 岭回归的基础中的异常现象 显示英文标题

标题： Anomalies in the Foundations of Ridge Regression

摘要： 霍尔和肯纳德（1970年）以及随后提出的岭回归基础中存在异常现象。传统的岭估计量及其性质并未如声称的那样通过拉格朗日方法约束解向量长度而得出。受此约束的估计量具有奇异分布；所提出的方法不一定是最小化的；并且此前未被发现的关于岭参数的界限也被揭示出来。大量关于估计、预测、交叉验证、选择岭参数及相关问题的文献，统称为岭回归，与约束优化或相应的不等式约束并不一致。问题可追溯到拉格朗日原理的误用、未能认识到分布的奇异性，以及约束与岭参数之间错误的联系。基于条件数的其他原则被证明可以验证传统的岭回归和替代的岭回归。数值研究表明，岭分析常常表现出它旨在解决的一些相同缺陷。 显示英文摘要

摘要： Anomalies persist in the foundations of ridge regression as set forth in Hoerl and Kennard (1970) and subsequently. Conventional ridge estimators and their properties do not follow on constraining lengths of solution vectors using LaGrange's method, as claimed. Estimators so constrained have singular distributions; the proposed solutions are not necessarily minimizing; and heretofore undiscovered bounds are exhibited for the ridge parameter. None of the considerable literature on estimation, prediction, cross--validation, choice of ridge parameter, and related issues, collectively known as ridge regression, is consistent with constrained optimization, nor with corresponding inequality constraints. The problem is traced to a misapplication of LaGrange's principle, failure to recognize the singularity of distributions, and misplaced links between constraints and the ridge parameter. Other principles, based on condition numbers, are seen to validate both conventional ridge and surrogate ridge regression to be defined. Numerical studies illustrate that ridge analysis often exhibits some of the same pathologies it is intended to redress.