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规模未知的有限总体均值与总量估计AI 解读

Problems of estimating the sum of metric values of a finite population of unknown number of elements are discussed for the case in which independent samples are available. Methods of point estimation applicable to the situation, frequent in economics, in which the samples are not simple random samples but rather are probability samples, with the sampling weights unknown, are investigated. Approximations to the expectation and variance of two alternative estimators are…

K 个随机变量乘积的方差AI 解读

An exact formula for the variance of the product of K random variables, x 1, x 2, ···, x K , is given as a function of the means and the central product-moments of the xi . The usual approximate variance formula for is compared with the exact formula; e.g., we note, in the case where the x i are mutually independent, that the approximate variance is too small, and that the relative accuracy of the approximation depends on the magnitude of the coefficients of variations of…

单侧与双侧截断正态样本参数估计的联合效率AI 解读

It is shown that the BAN (best asymptotically normal) estimates of μ the mean and σ the standard deviation of normal populations based on incomplete (singly or doubly truncated) samples of size n are asymptotically jointly less efficient than the corresponding estimates based on complete samples of the same size. The joint efficiency, e T (x α, x β), of the estimates based on incomplete samples is seen to be a monotonic function of the points of truncation x α and x β(x α <…

独立随机变量之和的概率不等式AI 解读

This paper proves a number of inequalities which improve on existing upper limits to the probability distribution of the sum of independent random variables. The inequalities presented require knowledge only of the variance of the sum and the means and bounds of the component random variables. They are applicable when the number of component random variables is small and/or have different distributions. Figures show the improvement on existing inequalities.

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利用辅助变量进行无偏估计的两种方法AI 解读

This paper shows the relationship between two existing methods of generating unbiased ratio and regression estimators. One procedure involves splitting up the population (theoretically) while the other splits up the sample itself. The two procedures yield similar estimators and are combinatorially equivalent. They are unalike in that they utilize different conditional arguments.

用迭代移动平均测量季节变化AI 解读

This paper presents a time-saving method for computing an iterated moving average with triangular weights to better represent the trend-cycle elements in a time-series for measuring seasonal variation. A printing-adding machine is used to obtain progressive summation of the Y-data values of a time series. A stencil having three suitably spaced slots is used to disclose progressively the three terms which are summed to obtain the graduated series required. Multiplied by the…

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基于成对观测样本的分布无关独立性检验AI 解读

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…

规模未知有限总体的均值与总量估计AI 解读

Problems of estimating the sum of metric values of a finite population of unknown number of elements are discussed for the case in which independent samples are available. Methods of point estimation applicable to the situation, frequent in economics, in which the samples are not simple random samples but rather are probability samples, with the sampling weights unknown, are investigated. Approximations to the expectation and variance of two alternative estimators are…

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单侧与双侧截断样本下正态总体参数估计的联合效率AI 解读

It is shown that the BAN (best asymptotically normal) estimates of μ the mean and σ the standard deviation of normal populations based on incomplete (singly or doubly truncated) samples of size n are asymptotically jointly less efficient than the corresponding estimates based on complete samples of the same size. The joint efficiency, e T (x α, x β), of the estimates based on incomplete samples is seen to be a monotonic function of the points of truncation x α and x β(x α <…

截断二项与负二项分布参数矩估计的渐近方差AI 解读

In this paper the asymptotic variances of method of moments estimates of the parameters of the truncated binomial and negative binomial distributions have been derived. For the binomial distribution with one class from the lower end of the distribution truncated, the efficiency of the estimate relative to maximum likelihood has been compared.

统计假设的逐层分解AI 解读

Let ω0 be the space of a parameter θ. Let ω i be a subset of ω i–1, i = 1, 2, ···, k, We test θ∈ω k against θ∈ω0 – ω k by testing iteratively the following hypotheses: θ∈ωi against θ∈ω i–1 – ω i , i = 1, 2, ···, k. The hypothesis θ∈ω k is accepted if and only if all of the intermediate hypotheses are accepted. If the test statistic for each intermediate hypothesis is based on the corresponding likelihood ratio λ i , we demonstrate why, under fairly general conditions, these…

迁移者—留守者模型的统计方法AI 解读

The mover-stayer model, a generalization of the Markov chain model, assumes that there are two types of individuals in the population under consideration: (a) the “stayer,” who with probability one remains in the same category during the entire period of study; (b) the “mover,” whose changes in category over time can be described by a Markov chain with constant transition probability matrix. The transition probability matrix for movers, and the proportion of stayers among…

分步最小二乘：残差分析与设定误差AI 解读

A stepwise procedure for estimating the parameters of the multiple linear regression model y = X 1β1 + X 2β2 + e is often used. Two articles in the March 1961 issue of this Journal focussed on the connection between the stepwise and the direct estimator of β2. The present paper spells out the connection between the stepwise and the direct estimator of β1, as a special case of Theil's analysis of specification error. A unified treatment of the two stepwise estimators is also…

随机区组设计中缺失小区处理程序的说明AI 解读

The properties of the missing plot procedure for a randomized block design are investigated from the randomization viewpoint. Expected mean squares, estimates of treatment effects, variances, and estimates of treatment effect variances are obtained when a particular block-plot combination is missing from the conceptual population of yields, when a block-treatment combination is missing, and when a restricted set of randomizations is considered. With proper definition of…

产业结构的统计分析：食品行业应用AI 解读

A stochastic model is used to analyze the changing size distributions of large firms in the food processing and chain store food distributing industries during 1948–1958. The model is shown to have certain predictive usefulness for anticipating changes in these distributions; however, the predictive value of the equilibrium distribution is questioned. An index of size mobility is developed from the model and the value of this index computed for each industry in each year and…

比较两个总体中二元特征的关联强度AI 解读

Asymptotically favorable methods for testing the equality of certain measures of association in different four-fold tables are deduced from the general theory of χ2-tests as given by Neyman and generalized by Anderson, Goodman and Gold. The tests turn out to be also obtainable by an intuitive use of maximum likelihood estimates as suggested by Wald's large sample theory and include one proposed by Lancaster for testing the second order interaction in a complex contingency…

回归扰动独立性的检验AI 解读

This article deals with the distribution of the Von Neumann ratio of least-squares estimated regression disturbances. This distribution is approximated by a beta distribution under the condition that the behaviour of explanatory variables of the regression over time is sufficiently smooth. Two examples are presented, together with a table containing 1 and 5 per cent significance limits for a number of observations ranging from 15 to 100 and a number of coefficients adjusted…