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若干非参数独立性检验的临界值与经验功效比较AI 解读

A class of nonparametric tests based on the third quadrant layer ranks has recently been studied by Woodworth [12] in connection with the problem of testing for independence in a bivariate distribution. In this article exact one-sided rejection regions are tabulated for the normal score layer rank test which is asymptotically locally most powerful for positive dependence in the bivariate normal distribution. The cut-off points are tabulated for sample sizes n = 4(1)9 and…

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最大与最小次序统计量近似独立所需的样本量AI 解读

Let Xn and X 1 be the largest and smallest order statistics, respectively, of a random sample of size n. Quite generally, Xn and X 1 are approximately independent for n sufficiently large. Minimum n for attaining at least specified levels of independence are developed. Level of independence is measured by the maximum difference between the true values of P(X 1 ≤x 1, Xn ≤xn ) and the corresponding values assuming independence of Xn and X 1. The results apply to all possible…

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选择最大均值总体问题的最优样本量AI 解读

Given k + 1 normal populations, identically distributed with a common known variance σ2 and unknown means, it is required to select N individuals in two stages as follows. In the first stage, n individuals are selected from each of the populations. In the second stage, the remaining N —n(k+1) individuals are selected from the population producing the largest mean in the first stage. A cost unique to the first stage is C(n) = c 0+c 1 na , where C 0, c 1 and α are positive…

混合样本的分析AI 解读

This article describes the application of the method of moments and the maximum likelihood method to identify the population of origin of each observation when it is thought that the data are a mixture of random observations from two different populations. Specifically, four cases in which both the populations belong to the binomial, the negative binomial, the Poisson or the hypergeometric family are discussed. Both methods also yield estimates of the parameters of the…

有限总体抽样的最优设计：批判性综述与新研究方向AI 解读

The design of sampling from finite populations is receiving increased attention in the statistical literature. This article presents a critical review of past studies and new developments and outlines areas meriting further study and research. Bayesian and non-Bayesian approaches are analyzed but are not offered in a normative manner. Both points of view and the extent to which they provide differences in survey sample design are discussed and examined. These differences are…

二项概率一致最强检验的序贯修改AI 解读

The early decision version of the uniformly most powerful (UMP) fixed-sample-size test for binomial probabilities, as described for instance by Alling [1], is modified by changing all continuation points which lie on or below a line with specified slope into acceptance points. The modification reduces the average sample number (ASN) for small values of the binomial probability with only a slight loss of power. Approximate formulas for the ASN and power function of the…

马尔可夫链阶数若干卡方检验的模拟评估AI 解读

This article reports a Monte Carlo evaluation of the levels of significance of chi-square tests for the order of two- and three-state Markov chains. Results are consistent with asymptotic theory only when samples are quite large.

利用家庭预算时间序列估计动态需求关系AI 解读

The demand parameters are estimated by fitting dynamic and static equations to a time series of Japanese multi-cross-section data using various methods. The results indicate that habit formation is predominant and income is much more important than prices and that it is worthwhile to use dynamic forms.

厂房与设备投资预期预测能力的重新评估AI 解读

This article suggests that anticipations alone do a better job of forecasting business plant and equipment expenditures than fitted functions which include only non-anticipatory data. Anticipations can also make a significant contribution in the presence of such data. Since previously published studies have come to different conclusions, the focus of this article is an evaluation of the methodology and results of those studies.

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基于单个特征根的两个协方差矩阵相等检验：功效比较AI 解读

Exact non-central distributions of individual characteristic roots have been obtained in two- and three-roots cases in connection with tests of the hypothesis σ1=σ2, where σ1 and σ2 are covariance matrices of two p-variate normal populations. Powers of tests using individual roots are tabulated for the test of this hypothesis against various one-sided simple alternatives and comparisons of powers made.

随机化序贯检验：截短单次抽样方案与序贯概率比检验的比较AI 解读

For Bernoulli random variables sequential tests of the simple hypotheses p=p 0 vs. p = p 1 are considered. In particular a comparison is made between the performance of sequential probability ratio tests (SPRTs) and curtailed single sampling plans (CSSPs), when both tests have the same error probabilities. In [1] it is shown that the CSSP has a strong optimality property. Nevertheless, if one admits randomized SPRTs, the latter are better. Numerical examples are considered…

用有序线性无偏最小方差估计量研究位置参数推断的稳健性AI 解读

Coefficients for computing ordered linear unbiased minimum variance (OLUMV) estimators of the location and scale parameters have been obtained for selected members of a class of symmetric power distributions which includes the normal, double exponential, and as a limiting case, the rectangular. Two examples are given illustrating how these coefficients may be used to study the sensitivity of inferences concerning location parameters to departure from normality. The first…

逆线性回归的贝叶斯视角AI 解读

The model considered in this paper is simple linear regression , and the problem is to make statistical inferences about an unknown value of x corresponding to one or more additional observed values of y. The maximum likelihood estimator x of x and the classical (1 - α) 100% confidence set S for x have some undesirable properties. For example, has infinite mean square error and > 0. The purpose of this paper is to demonstrate that insight and understanding, as well as a…

允许平局的 Bradley–Terry 配对比较模型扩展AI 解读

This study is concerned with the extension of the Bradley-Terry model for paired comparisons to situations which allow an expression of no preference. A new model is developed and its performance compared with a model proposed by Rao and Kupper. The maximum likelihood estimates of the parameters are found using an iterative procedure which, under a weak assumption, converges monotonically to the solution of the likelihood equations. It is noted that for a balanced paired…

二元治疗反应下的两种疗法选择AI 解读

A decision theoretic approach to the design of a clinical trial is considered for the situation in which a total of N patients with a disease receive one of two treatments and the responses to the treatments are dichotomous. Two costs are considered: The cost of treating a patient with the inferior treatment and the cost of conducting the trial. Minimax and Bayes procedures are used to determine the optimum size of a fixed sample trial. Bayes solutions for the optimum sample…

等概率多项分布下卡方与似然比统计量的精确分布AI 解读

A sample of size N is taken from an equiprobable t-category multinomial distribution. The precise values of Pearson's X 2 and the likelihood ratio statistic A were computed for t = 3(1)6, N = 3(1)12; t = 6(1)14, N = 6(1)2t; t=15(1)18, N = 6(1)28. The logarithms of the tail areas were smoothed and fitted by means of quadratic expressions. Much information is given concerning the accuracy of the chi-squared fits to the distributions of X 2 and A. A table of −log10 P(χ2 > a) is…

定性数据的多元分析：多重分类中的交互作用AI 解读

For the m-way contingency table, we discuss both the direct estimation of the multiplicative interactions among the m variables, and the indirect testing of hypotheses pertaining to these interactions. We consider, among other things, hierarchical hypotheses pertaining to the interactions among the m variables, including hypotheses that can be expressed in terms of one or more of the following kinds of concepts: (a) the usual concepts of independence and equiprobability; (b)…