Minimax Ridge Regression Estimation.

Abstract

The technique of ridge regression has become a popular tool for data analysts faced with a high degree of multicollinearity in their data. By using a ridge estimator, it was hoped that one could both stabilize the estimates (lower the condition number of the design matrix) and improve upon the squared error loss of the least squares estimator. Recently classes of ridge regression estimators have been developed which dominate the usual estimator in risk, and hence are minimax. This paper derives conditions that are necessary and sufficient for minimaxity of a large class of ridge regression estimators. The conditions derived here are very similar to those derived for minimaxity of some Stein-type estimators.

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Document Details

Document Type
Technical Report
Publication Date
May 01, 1977
Accession Number
ADA043489

Entities

People

  • George Casella

Organizations

  • Purdue University

Tags

DTIC Thesaurus Topics

  • Air Force
  • Covariance
  • Data Science
  • Deficiencies
  • Eigenvalues
  • Eigenvectors
  • Estimators
  • Inequalities
  • Information Science
  • Normal Distribution
  • Notation
  • Observation
  • Random Variables
  • Scientific Research
  • Statistical Analysis
  • Statistics

Fields of Study

  • Mathematics

Readers

  • Regression Analysis.