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Non-Parametric Theory: Scale and Location Parameters

Published online by Cambridge University Press:  20 November 2018

D. A. S. Fraser
D. A. S. Fraser*
Affiliation:
University of Toronto
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In §2 a result in measure theory is obtained. The remainder of this paper, §3 to §11, contains results in the branch of statistics called non-parametric theory; these results in part are based on the measure result of §2.

The measure result concerns a class of probability distributions—those distributions having a probability density function on the real line and for which a fraction p of the probability is on the negative axis and a fraction q = 1 - p is on the positive axis. Corresponding to a sample of n the functional form is obtained for a statistic having expectation zero for all distributions in the class; such a statistic is referred to as an unbiased estimate of zero.

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 6 , 1954 , pp. 46 - 68
Copyright
Copyright © Canadian Mathematical Society 1954

References

1. Halmos, P., The theory of unbiased estimation, Ann. Math. Stat., 17 (1946), 34–43.Google Scholar
2. Lehmann, E. L., Notes on the theory of estimation, Lecture notes mimeographed at the University of California.Google Scholar
3. Fraser, D. A. S., Completeness of order statistics, Can. J. Math., 6 (1954), 42–45.Google Scholar
4. Lehmann, E. L. and Stein, C., Most powerful tests of composite hypotheses. I: Normal distributions, Ann. Math. Stat., 15(1948), 495–516.Google Scholar
5. Lehmann, E. L. and Stein, C., On the theory of some non-parametric hypotheses, Ann. Math. Stat. 20 (1949), 28–45.Google Scholar
6. Robbins, H., On distribution-free tolerance limits in random sampling, Ann. Math. Stat., 15 (1944), 214–217.Google Scholar
7. Scheffé, H. and Tukey, J. W., Nonparametric estimation. I: Validation of order statistics, Ann. Math. Stat., 16(1945), 187–192.Google Scholar
8. Lehmann, E. L. and Scheffé, H., Completeness, similar regions, and unbiased estimation, Sankhya, 10 (1950), 305–340.Google Scholar
9. Wilcoxen, F., Individual comparisons by ranking methods, Biometrics, 1 (1945), 80–83.Google Scholar