Statistical Inference for Means

  • Bernard Flury
Part of the Springer Texts in Statistics book series (STS)


In this chapter we study selected problems of hypothesis testing and confidence regions in multivariate statistics. We will focus mostly on T 2-tests, or Hotelling’s T 2, after the statistician Harold Hotelling (1895–1973). In the spirit of this book, which emphasizes parameter estimation more than testing, we will give rather less attention to aspects of hypotheses testing than traditional textbooks on multivariate statistics. In particular, we will largely ignore problems like optimality criteria or power of tests. Instead, we will focus on a heuristic foundation to the T 2-test methodology, for which we are well prepared from Chapter 5.


Discriminant Function Null Distribution Confidence Region Likelihood Ratio Statistic Sample Covariance Matrix 
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Suggested Further Reading

  1. Casella, G., and Berger, R.L. 1990. Statistical Inference. Belmont, CA: Duxbury Press.zbMATHGoogle Scholar
  2. Silvey, S.D. 1975. Statistical Inference. London: Chapman and Hall.zbMATHGoogle Scholar
  3. Hotelling, H. 1931. The generalization of Student’s ratio. Annals of Mathematical Statistics 2, 360–378.CrossRefGoogle Scholar
  4. Rao, C.R. 1948. Tests of significance in multivariate analysis. Biometrika 35, 58–79.MathSciNetzbMATHGoogle Scholar
  5. Takemura, A. 1985. A principal decomposition of Hotelling’s T2 statistic. In Multivariate Analysis VI, P.R. Krishnaiah, ed. Amsterdam: Elsevier, pp. 583–597.Google Scholar
  6. Fairley, D. 1986. Cherry trees with cones? The American Statistician 40, 138–139.Google Scholar
  7. Mardia, K.V., Kent, J.T., and Bibby, J.M. 1979. Multivariate Analysis. London: Academic Press.zbMATHGoogle Scholar
  8. Rao, C.R. 1970. Inference on discriminant function coefficients. In Essays in Probability and Statistics, R.C. Bose et al., eds. Chapel Hill: University of North Carolina Press, pp. 587–602.Google Scholar
  9. Roy, S.N. 1957. Some Aspects of Multivariate Analysis. New York: Wiley.Google Scholar
  10. Efron, B., and Tibshirani, R. 1993. An Introduction to the Bootstrap. London: Chapman and Hall.zbMATHGoogle Scholar
  11. Ripley, B.D. 1987. Stochastic Simulation. New York: Wiley.zbMATHCrossRefGoogle Scholar
  12. Ross, S. 1996. Simulation, 2nd ed. London: Academic Press.Google Scholar
  13. Westfall, P.H., and Young, S.S. 1993. Resampling—Based Multiple Testing. New York: Wiley.Google Scholar

Copyright information

© Springer Science+Business Media New York 1977

Authors and Affiliations

  • Bernard Flury
    • 1
  1. 1.Department of MathematicsIndiana UniversityBloomingtonUSA

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