Statistical Inference for Means
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.
KeywordsDiscriminant Function Null Distribution Confidence Region Likelihood Ratio Statistic Sample Covariance Matrix
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Suggested Further Reading
- 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
- Fairley, D. 1986. Cherry trees with cones? The American Statistician 40, 138–139.Google Scholar
- 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
- Roy, S.N. 1957. Some Aspects of Multivariate Analysis. New York: Wiley.Google Scholar
- Ross, S. 1996. Simulation, 2nd ed. London: Academic Press.Google Scholar
- Westfall, P.H., and Young, S.S. 1993. Resampling—Based Multiple Testing. New York: Wiley.Google Scholar