5. Unbiased and Invariant Tests

  1. Seymour Geisser

Published Online: 5 JAN 2006

DOI: 10.1002/0471743135.ch5

Modes of Parametric Statistical Inference

Modes of Parametric Statistical Inference

How to Cite

Geisser, S. (2005) Unbiased and Invariant Tests, in Modes of Parametric Statistical Inference, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/0471743135.ch5

Author Information

  1. Department of Statistics, University of Minnesota, Minneapolis, USA

Publication History

  1. Published Online: 5 JAN 2006
  2. Published Print: 9 SEP 2005

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: 9780471667261

Online ISBN: 9780471743132



  • unbiased (UMPU) and invariant (UMPI) tests;
  • invariant tests;
  • Likelihood Ratio Test (LRT) criterion


This chapter contains sections titled:

  • Unbiased Tests

  • Admissibility and Tests Similar on the Boundary

  • Neyman Structure and Completeness

  • Invariant Tests

  • Locally Best Tests

  • Test Construction

  • Remarks on N-P Theory

  • Further Remarks on N-P Theory

  • Law of the Iterated Logarithm (LIL)

  • Sequential Analysis

  • Sequential Probability Ratio Test (SPRT)

  • References