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基于两阶段抽样、满足预设方差上界的二项与泊松参数估计AI 解读

The problem of unbiased estimation of the parameter θ in the binomial and Poisson distributions is considered. The variance of the estimate is required not to exceed a preassigned bound, B. For the Poisson distribution this can be achieved only by sequential sampling and also in the binomial case sequential sampling may reduce the expected sample size. Here only two-stage sampling is considered. The methods of estimation discussed differ from earlier considered two-stage…

联立方程估计量对模型随机假设的敏感性AI 解读

The paper reports the results of several sampling experiments investigating the sensitivity of various simultaneous-equations estimators to errors in the exogenous variables, stochastic coefficients, heteroskedastic disturbances and auto correlated disturbances. The estimates studied are direct least squares, two-stage least squares, Nagar's unbiased k-class estimator, limited-information maximum likelihood, three-stage least squares, and full-information maximum likelihood.…

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多项试验中线性与对数线性假设的局部渐近最强检验AI 解读

We derive Neyman's locally asymptotically most powerful test criterion to test a linear hypothesis, and in particular, obtain such criteria to test linear hypotheses in binomial and multinomial experiments. We also discuss testing log-linear hypotheses in the parameters of a multinomial experiment, and give a simple criterion for testing the hypothesis of no second order interaction in a p × q × r (p, q, r, > 2) contingency table. Asymptotic tests of the hypotheses mentioned…

非线性参数函数的区间估计（三）AI 解读

Let f(μ1, μ2) = constant be a function which is monotone and has no finite termini in the (μ1, μ2) plane. Let x 1 and x 2 be either independent normal with unknown means μ1, μ2 and unknown variances σ2 1, σ2 2 or correlated normal with unknown mean vector (μ1, μ2) and unknown variance matrix σ. Suppose, in the first instance, that estimates, s 2 1 and s 2 2, of σ2 1 and σ2 2 with v 1 and v 2 degrees of freedom are available and, in the second instance, an estimate, S, of σ…

若干 Behrens–Fisher 型回归问题的 Scheffé 型检验AI 解读

In educational and psychological applications as well as in other applications, it may be necessary to make certain comparisons of two regression lines when the variances are unequal. Such problems arise, for example, in studies comparing two alternative curriculums or two different teaching methods. By generalizing an idea which Scheffé used to obtain a test for the Behrens-Fisher problem, this paper develops some tests for comparing two regression lines when the two sets…

两样本秩检验的百分位修正AI 解读

This paper presents a simple method for increasing the limiting Pitman efficiency of rank tests relative to the best tests for samples normal distributions without using complicated scoring systems. Our proposal is to select two numbers p and r (0 < p, r < 1) and then score, with integer weights, the data in the top p th and bottom r th fractions of the combined sample. The percentile modified tests for scale are quite effective. When p = r = 1/8 (i.e., we score only the…

若干两样本非参数检验AI 解读

A family of two-sample non-parametric tests is described, in which only the tails of the distributions are used. Some are presented as tests of dispersion and some as tests of location. Critical values for certain of the tests are given for large samples. The power of the tests is discussed, and fresh results are given for a test of dispersion against rectangular alternatives.

一种贝叶斯无差别先验构造程序AI 解读

In a logical probability approach to inference, distributions on a parameter space are interpretable as representing states of knowledge, and any prevailing state of knowledge may be taken to have been arrived at from a previous state of ignorance (indifference) followed by an accumulation of prior data. In this paper an indifference procedure is introduced that requires postulating what size and what kind of samples will and will not (in a special sense) permit statistical…

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分块矩阵求逆法在非正交数据分析中的应用AI 解读

A special form of a partitioned matrix, similar to Greenberg and Sarhan's, is used to invert it. This method is here shown to be useful in the analysis of some non-orthogonal connected designs.

概率论在刑事科学中的应用（二）AI 解读

A general model for the evaluation of partial transfer evidence is developed in this article. This model is less restrictive than were the original models presented in an earlier paper, thus allowing it to be applied to a more general class of situations. A Bayesian approach to the problem of evidence evaluation is explored, and the probability of error calculated in the Bayesian model is shown to be a reasonable approximation to the probability of possible error calculated…

分析性调查的双重抽样方案AI 解读

The concept of analytical sample surveys is discussed in general, and a double sampling scheme is proposed for certain situations. Emphasis is placed on the presentation of a method which can be used to solve a certain class of problems. It is assumed that the subgroups of the population which are to be compared form a one-way classification, and are not identifiable in advance of drawing a simple random sample from the population. With double sampling, a large sample is…

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分块矩阵求逆方法在非正交数据分析中的应用AI 解读

A special form of a partitioned matrix, similar to Greenberg and Sarhan's, is used to invert it. This method is here shown to be useful in the analysis of some non-orthogonal connected designs.

非线性参数函数的区间估计（三）AI 解读

Let f(μ1, μ2) = constant be a function which is monotone and has no finite termini in the (μ1, μ2) plane. Let x 1 and x 2 be either independent normal with unknown means μ1, μ2 and unknown variances σ2 1, σ2 2 or correlated normal with unknown mean vector (μ1, μ2) and unknown variance matrix σ. Suppose, in the first instance, that estimates, s 2 1 and s 2 2, of σ2 1 and σ2 2 with v 1 and v 2 degrees of freedom are available and, in the second instance, an estimate, S, of σ…

若干两样本非参数检验AI 解读

A family of two-sample non-parametric tests is described, in which only the tails of the distributions are used. Some are presented as tests of dispersion and some as tests of location. Critical values for certain of the tests are given for large samples. The power of the tests is discussed, and fresh results are given for a test of dispersion against rectangular alternatives.

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