Regression with strongly correlated data

  • Authors:

  • Christopher S. Jones;John M. Finn;Nicolas Hengartner

  • Affiliations:

  • T-15, Plasma Theory, Los Alamos National Laboratory, Los Alamos, NM 87545, United States;T-15, Plasma Theory, Los Alamos National Laboratory, Los Alamos, NM 87545, United States;CCS-3, Information Sciences, Los Alamos National Laboratory, Los Alamos, NM 87545, United States

  • Venue:
  • Journal of Multivariate Analysis
  • Year:
  • 2008

Quantified Score

Hi-index 0.00

Visualization

Abstract

This paper discusses linear regression of strongly correlated data that arises, for example, in magnetohydrodynamic equilibrium reconstructions. We have proved that, generically, the covariance matrix of the estimated regression parameters for fixed sample size goes to zero as the correlations become unity. That is, in this limit the estimated parameters are known with perfect accuracy. Simple examples are shown to illustrate this effect and the nature of the exceptional cases in which the covariance of the estimate does not go to zero.