Generalized Inverses, Ridge Regression, Biased Linear Estimation, and Nonlinear Estimation

1970/08/01 by Donald W. Marquardt · 865 citations
Computer Science · Engineering · Mathematics · #Applied mathematics #Control Systems and Identification #Economics #Estimation #Geology #Linear regression #Mathematics #Neural Networks and Applications #Nonlinear regression #Nonlinear system #Physics #Regression #Regression analysis #Ridge #Statistical and numerical algorithms #Statistics

paper · doi:10.1080/00401706.1970.10488699

published in Technometrics 12(3), 591-612 (Taylor & Francis)

openalex publication_date 1970/08/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06

Abstract

A principal objective of this paper is to discuss a class of biased linear estimators employing generalized inverses. A second objective is to establish a unifying perspective. The paper exhibits theoretical properties shared by generalized inverse estimators, ridge estimators, and corresponding nonlinear estimation procedures. From this perspective it becomes clear why all these methods work so well in practical estimation from nonorthogonal data.

Citations

• Ridge Regression: Applications to Nonorthogonal Problems
• Ridge Regression: Biased Estimation for Nonorthogonal Problems

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