FIVE. Variance Matrices of Estimators of Regression Coefficients

  1. Mari Palta

Published Online: 11 AUG 2003

DOI: 10.1002/0471467979.ch5

Quantitative Methods in Population Health: Extensions of Ordinary Regression

Quantitative Methods in Population Health: Extensions of Ordinary Regression

How to Cite

Palta, M. (2003) Variance Matrices of Estimators of Regression Coefficients, in Quantitative Methods in Population Health: Extensions of Ordinary Regression, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/0471467979.ch5

Author Information

  1. Madison, Wisconsin, USA

Publication History

  1. Published Online: 11 AUG 2003
  2. Published Print: 15 AUG 2003

Book Series:

  1. Wiley Series in Probability and Statistics

Book Series Editors:

  1. Walter A. Shewhart and
  2. Samuel S. Wilks

ISBN Information

Print ISBN: 9780471455059

Online ISBN: 9780471467977

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Keywords:

  • standard error;
  • least squares;
  • linear transformation;
  • maximum likelihood;
  • information matrix;
  • large sample variance;
  • Wald test;
  • likelihood ratio test;
  • Type 1;
  • Type 3

Summary

We use the variance formula for a linear transformation to derive the variance matrix of least squares estimators. Information matrix is introduced and used to derive the variance of maximum likelihood estimators based on the error term being normally distributed. The use of the variance estimators for tests and confidence intervals is discussed. The special case of one predictor is derived in detail and similarity of the variances based on least squares and maximum likelihood is demonstrated. Results from PROC REG and PROC MIXED as well as some basic features of the two procedures are compared. Systolic blood pressure is regressed on age BMI and gender.