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Linear regression analysis using the relative squared error

Authors
Journal
Linear Algebra and its Applications
0024-3795
Publisher
Elsevier
Publication Date
Volume
354
Identifiers
DOI: 10.1016/s0024-3795(01)00572-9
Keywords
  • Linear Affine Estimator
  • Linear Affine Predictor
  • Linear Regression
  • Löwner Ordering
  • Minimax Principle
  • Ridge Regression

Abstract

Abstract In order to determine estimators and predictors in a generalized linear regression model we apply a suitably defined relative squared error instead of the most frequently used absolute squared error. The general solution of a matrix problem is derived leading to minimax estimators and predictors. Furthermore, we consider an important special case, where an analogon to a well-known relation between estimators and predictors holds and where generalized least squares estimators as well as Kuks–Olman and ridge estimators play a prominent role.

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