Type: Article
Publication Date: 1954-01-01
Citations: 20
DOI: https://doi.org/10.4153/cjm-1954-007-7
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.