Numerical Computations for Univariate Linear Models

Abstract

The authors consider the usual univariate linear model E(y) = Xgamma, V(y) = Sigma squared. In part one of the paper X has full column rank. Numerically stable and efficient computational procedures are developed for the least squares estimation of gamma and the error sum of squares. An orthogonal triangular decomposition of X is used, using Householder transformations. A lower bound for the condition number of X is immediately obtained from this decomposition. In part two, X has less than full rank. Least squares estimates are obtained using generalized inverses. The function L'gamma is estimable whenever it admits an unbiased esimator linear in y.

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1971
Accession Number
AD0737648

Entities

People

  • Gene H. Golub
  • George P. H. Styan

Organizations

  • Stanford University

Tags

Communities of Interest

  • C4I
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Analysis Of Variance
  • Computations
  • Computer Programming
  • Computer Programs
  • Computers
  • Data Science
  • Decomposition
  • Errors
  • Estimators
  • Information Science
  • New York
  • Regression Analysis
  • Square Roots
  • Statistical Algorithms
  • Statistics
  • Universities

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Linear Algebra
  • Regression Analysis.