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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…

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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…

调整类别差异的多元线性回归分析AI 解读

A method is described for solving by iteration the normal equations in multiple linear regression analysis when class differences are present, and a proof is given of the convergence of the process. Comparison is made with a direct method of solution in which the information matrix is adjusted for class differences before it is inverted.

截断分组双曲正割平方分布的位置与尺度参数估计AI 解读

The iterative calculations required to obtain the maximum likelihood estimates of α and β in the distribution function dF(z) = e z /(1 + e z )2 dz, where z = α +βx, are presented for doubly truncated, upper and lower truncated, and untruncated grouped samples. The calculations needed to obtain the maximum likelihood estimator of Pareto's constant are also given for a lower truncated grouped sample with both equal and unequal grouping. Asymptotic variances and covariances are…

方差下界的另一面：一则附有更正的札记AI 解读

This note has as its primary purpose the correction of a statement made in a previous paper regarding the attainment of the variance of a proposed estimator of its lower bound. At the same time it seemed useful, as an expository function, to recapitulate a development of the lower bound which led this writer to a better understanding of it, and to the realization of the indicated error. Here the bound is developed ab initio from a simple identity, instead of secondarily from…

双变量均含误差时的直线拟合与预测AI 解读

Define the linear structural relation with parameters α, β, by μ = α +βv. This paper considers the problem of confidence region estimation of α and β based on a sample of independent pairs, (y i , x i ), i = 1, 2, ···, with Ey i = μi, Ex i = v i . The pairs (y i , x i ) are assumed to have a common (unknown) covariance matrix and to follow the bivariate normal distribution. Point estimates subject only to and that the choice of the l i be independent of the actual…

经济时间序列相关系数的分布AI 解读

This paper presents results, mainly in tabular form, of a sampling experiment in which 100 economic time series 25 years long were drawn at random from the Historical Statistics for the United States. Sampling distributions of coefficients of correlation and autocorrelation were computed using these series, and their logarithms, with and without correction for linear trend. We find that the frequency distribution of autocorrelation coefficients has the following properties:…

置信区间的长度AI 解读

The expected length of a confidence interval is shown to equal the integral over false values of the probability each false value is included. Thus two desiderata for choosing among confidence procedures lead to the same measure of desirability. Furthermore, by common definitions of “optimum,” a procedure is optimum as regards including false values if and only if it is optimum as regards expected length. However, the procedure with minimum expected length ordinarily depends…

混合指数响应规律的估计AI 解读

This paper is concerned with the estimation of the parameters of a mixed-exponential response law, given some sample observations. Two alternative laws are considered, each having two parameters. The first law expresses the proportion F(t) of the population who have responded within time t in the form F(t) = (1 – e −αt )ξ. The second law states that F(t) = 1 – (1 + λt)−v. The problem has been encountered in the context of market research, in estimating the “penetration” of a…

Mann–Whitney–Wilcoxon 统计量渐近正态性的简注AI 解读

The Mann-Whitney-Wilcoxon statistic is of some importance in non-parametric statistical inference. The asymptotic normality of this statistic has been established previously for the case where the distributions of the random variables, in each of the two samples, are the same. In the present work it is shown that this statistic is asymptotically normal when these distributions are not all the same. An application of this result to a particular hypothesis testing problem is…

两个典型过度识别情形下广义经典线性估计量的精确有限样本分布AI 解读

The asymptotic unbiasedness and normality of alternative statistical estimators θ, θ,1 ··· of a given parameter θ* are generally proved without reference to any explicit knowledge of the exact finite sample distribution functions, F n (x), G n (x) ···. (Here n denotes sample size.) Within the class of asymptotically unbiased and normally distributed estimators of a given parameter it is sometimes possible to demonstrate that one estimator possesses a smaller asymptotic…

调整类别差异的多元线性回归分析AI 解读

A method is described for solving by iteration the normal equations in multiple linear regression analysis when class differences are present, and a proof is given of the convergence of the process. Comparison is made with a direct method of solution in which the information matrix is adjusted for class differences before it is inverted.

方差下界的另一面：一则更正札记AI 解读

This note has as its primary purpose the correction of a statement made in a previous paper regarding the attainment of the variance of a proposed estimator of its lower bound. At the same time it seemed useful, as an expository function, to recapitulate a development of the lower bound which led this writer to a better understanding of it, and to the realization of the indicated error. Here the bound is developed ab initio from a simple identity, instead of secondarily from…

两个变量均含误差时的直线拟合与预测AI 解读

Define the linear structural relation with parameters α, β, by μ = α +βv. This paper considers the problem of confidence region estimation of α and β based on a sample of independent pairs, (y i , x i ), i = 1, 2, ···, with Ey i = μi, Ex i = v i . The pairs (y i , x i ) are assumed to have a common (unknown) covariance matrix and to follow the bivariate normal distribution. Point estimates subject only to and that the choice of the l i be independent of the actual…

经济时间序列相关系数的分布AI 解读

This paper presents results, mainly in tabular form, of a sampling experiment in which 100 economic time series 25 years long were drawn at random from the Historical Statistics for the United States. Sampling distributions of coefficients of correlation and autocorrelation were computed using these series, and their logarithms, with and without correction for linear trend. We find that the frequency distribution of autocorrelation coefficients has the following properties:…

混合指数响应规律的估计AI 解读

This paper is concerned with the estimation of the parameters of a mixed-exponential response law, given some sample observations. Two alternative laws are considered, each having two parameters. The first law expresses the proportion F(t) of the population who have responded within time t in the form F(t) = (1 – e −αt )ξ. The second law states that F(t) = 1 – (1 + λt)−v. The problem has been encountered in the context of market research, in estimating the “penetration” of a…

摘要暂缺

关于 Mann–Whitney–Wilcoxon 统计量渐近正态性的注记AI 解读

The Mann-Whitney-Wilcoxon statistic is of some importance in non-parametric statistical inference. The asymptotic normality of this statistic has been established previously for the case where the distributions of the random variables, in each of the two samples, are the same. In the present work it is shown that this statistic is asymptotically normal when these distributions are not all the same. An application of this result to a particular hypothesis testing problem is…

抽样理论中的随机舍入扩张因子AI 解读

In a large scale survey, where a non-self-weighting design is used, the work at the tabulation stage becomes time consuming and costly due to the large number of multipliers (inflation factors) involved in obtaining the estimates. In this paper a technique is developed to substitute the multipliers by a very small number of multipliers called “randomized rounded-off multipliers” by a suitable randomizing process, thereby reducing the work at the tabulation stage. A suitable…

奥斯卡·安德森的统计学工作AI 解读

T HE death of Professor Oskar Anderson in Munich, Germany on February 12, 1960 in his 73rd year is a great loss for statisticians everywhere. Professor Anderson was born on August 2, 1887 in Minsk, Russia. He studied mathematics, physics, economics, and law at the Universities of Kasan and St. Petersburg (Leningrad). He was an assistant of the well known Russtian statistician A. A. Tschuprow. He taught mathematical statistics at the High School of Commerce in Kasan, later at…

泊松过程的多元回归分析AI 解读

A multiple regression model based on the Poisson density is discussed. Point estimation by maximum likelihood results in estimating equations which can be solved by iteration based on scoring or on a successively revised weighted least squares estimator. The first round of each iterative process is shown to be BAN, provided that the ordinary least squares estimator is used as the initial condition. A minimum chi-squared estimator, which can be computed directly from sample…