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A Distribution-Free Test of Independence with a Sample of Paired Observations
基于配对观测样本的分布无关独立性检验
A distribution-free test of the hypothesis that identically distributed paired observations are independent may be based on a test statistic, D, which measures the variation between the ranks in each pair of observations. Examples of applications of this proposed test are discussed. Further, since the statistic is related to the one used in the Kruskal-Wallis H-test applied to samples of 2, some results are of interest for what they suggest about the H-test. Properties of…
A Distribution-Free Test of Independence with a Sample of Paired Observations
基于成对观测样本的分布无关独立性检验
A distribution-free test of the hypothesis that identically distributed paired observations are independent may be based on a test statistic, D, which measures the variation between the ranks in each pair of observations. Examples of applications of this proposed test are discussed. Further, since the statistic is related to the one used in the Kruskal-Wallis H-test applied to samples of 2, some results are of interest for what they suggest about the H-test. Properties of…
Estimators for the Product of Arithmetic Means
总体算术均值乘积的估计量
SUMMARY Symmetric functions which provide unbiased estimators for the product of m population arithmetic means are considered for two sampling procedures: (a) m independently selected simple random samples, and (b) a simple random sample of multivariate observations. Formulae for the variances of these estimators and for estimated variances are derived.
On estimators for variances and covariances
An Unbiased Estimator for Powers of the Arithmetic Mean
算术平均数幂的无偏估计量
SUMMARY An unbiased estimator for integral powers of the arithmetic mean, when sampling with replacement, is given, together with a formula for its variance and an unbiased estimator for this variance. Similar results are given for functions which can be expressed as a series in powers of the mean.
On the Problem of Matching Lists by Samples
通过抽样匹配名单的问题
This paper presents theory for estimation of the proportions of names common to two or more lists of names, through use of samples drawn from the lists. The theory covers (a) the probability distributions, expected values, variances, and the third and fourth moments of the estimates of the proportions duplicated; (b) testing a hypothesis with respect to a proportion; (c) optimum allocation of the samples; (d) the, effect of duplicates within a list; (e) possible gains from…
On the Problem of Matching Lists by Samples
通过抽样估计名单重合比例的问题
This paper presents theory for estimation of the proportions of names common to two or more lists of names, through use of samples drawn from the lists. The theory covers (a) the probability distributions, expected values, variances, and the third and fourth moments of the estimates of the proportions duplicated; (b) testing a hypothesis with respect to a proportion; (c) optimum allocation of the samples; (d) the, effect of duplicates within a list; (e) possible gains from…