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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.

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

References

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