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Large sample tests of statistical hypotheses concerning several parameters with applications to problems of estimation

Published online by Cambridge University Press:  24 October 2008

C. Radhakrishna Rao
C. Radhakrishna Rao
Affiliation:
King's CollegeCambridge
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Extract

If the probability differential of a set of stochastic variates contains k unknown parameters, the statistical hypotheses concerning them may be simple or composite. The hypothesis leading to a complete specification of the values of the k parameters is called a simple hypothesis, and the one leading to a collection of admissible sets a composite hypothesis. In this paper we shall be concerned with the testing of these two types of hypotheses on the basis of a large number of observations from any probability distribution satisfying some mild restrictions and their use in problems of estimation.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 44 , Issue 1 , January 1948 , pp. 50 - 57
Copyright
Copyright © Cambridge Philosophical Society 1948

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References

REFERENCES

Bernstein, F.Zusammenfassende Betrachtungen über die erblichen Blutstrukturen des Menschen. Z. indukt. Abstamm.- u. VererbLehre, 37 (1925), 237–70.Google Scholar
Doob, J. L.Probability and statistics. Trans. Amer. Math. Soc. 36 (1934), 759–75.CrossRefGoogle Scholar
Fisher, R. A.The detection of linkage with dominant abnormalities. Ann. Eugen., London, 6 (1935), 187–201.CrossRefGoogle Scholar
Fisher, R. A.The logical inversion of the notion of the random variable. Sankhyä, 7 (1945), 130–3.Google Scholar
Fisher, R. A.A system of scoring linkage data with special reference to pied factors in mice. Amer. Nat. 80 (1946), 568–78.CrossRefGoogle ScholarPubMed
Kosambi, D. D.The estimation of map distance from recombination values. Ann. Eugen. London, 12 (1944), 172–6.CrossRefGoogle Scholar
Rao, C. R. and Poti, S. J.On locally most powerful tests when alternatives are one sided. Sankhyä, 7 (1946), 439.Google Scholar
Rao, C. R.Minimum variance and the estimation of several parameters. Pro'c. Cambridge Phil. Soc. 43 (1947), 280–3.CrossRefGoogle Scholar
Wald, A.Some examples of asymptotically most powerful tests. Ann. Math. Stat. 12 (1941), 396–408.CrossRefGoogle Scholar
Wald, A.Tests of statistical hypotheses concerning several parameters when the number of observations is large. Trans. Amer. Math. Soc. 54 (1943), 426–82.CrossRefGoogle Scholar
Wilks, S. S.Optimum fiducial regions for simultaneous estimation of several population parameters from large samples. Ann. Math. Statist. 10 (1939), 85.Google Scholar