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等概率检验及其在若干同时推断问题中的应用AI 解读

Consider the problem of testing the hypothesis H 0: θ ∈ W 0 against the alternative H 1: θ ∈ W 1 when a certain subset E 0 ⊂ W 1 is given. This subset E 0 is such that the risk of accepting H 0 will be significant economically only if θ ∈ E 0. For this problem a test obtained by generalising the equal probability test of Arrow (1960) is suggested. Applications of the test procedure to the problems of combining several independent tests and of comparing several populations…

中位显著性水平及其他小样本检验效能指标AI 解读

The concepts of the “median significance level” (MSL) and the “significance level of the average” (SLA) are introduced and some relationships among these measures and the recently introduced “expected significance level” (ESL), “average critical value” (ACV), and “median critical value” (MCV) are considered. The median significance level is defined as the median of the distribution of the observed significance level for a given alternative and is shown to be equivalent to…

论一种受约束最小二乘估计量AI 解读

The method of Sweep-Out is used to obtain computing formulas for calculating the least-squares estimator and its variance matrix in linear models, not necessarily of full rank, in which certain restrictions may hold on the actual parameters. A test for a specified value of parametric restrictions is also discussed.

BLUS估计的一则札记AI 解读

For the classical linear model, Theil and Koerts developed the so-called best linear unbiased scalar-variance-matrix (BLUS) estimator. In this note a theorem on the variance matrix of the BLUS estimation errors will be proved. A new derivation will be given for “price” and “efficiency” of the estimator, as defined by Koerts.

用 Aitken 估计量分配预定总量AI 解读

The problem considered in this paper is one of allocating a predetermined aggregate among its components. An example from econometrics is the allocation among various competing consumption items of a consumer's budget, the total size of which is usually taken as determined outside the allocation framework. Under the specification adopted, one may treat any choice of (m — 1) of the m components of the predetermined aggregate as stochastic, fitting the allocation equations for…

若干Rényi型统计量的有限样本临界值表AI 解读

Let X(1) ≤ X (2) ≤ … ≤ X (n) be an ordered sample of a random variable X which has continuous probability distribution function F (x), and let Fn (x) be the corresponding empirical distribution function. The following three statistics, introduced by A. Rényi, are considered: The paper presents table of exact probabilities for these statistics for finite sample sizes. The limiting distributions of these statistics for sample size n ∞ are discussed, and sample sizes are…

非正则估计（一）：位置参数估计量的方差界AI 解读

Maximum likelihood and other BAN estimators have been shown to possess certain optimal asymptotic properties in estimating the parameters of probability distributions satisfying specific regularity conditions. The subject of non-regular estimation is concerned with problems in which these conditions do not hold. In many such problems, classical lower bounds on the variance of unbiased estimators, such as the Cramér-Rao bound, lead to the trivial result V(t) ≧0, where t is…

证明矩阵相等的一个引理及其最小二乘型二次型应用AI 解读

A useful lemma for proving the equality of two matrices is given. The result is then applied to proving the equality of certain quadratic forms arising in least squares models.

矩阵微分的若干定理：特别关注 Kronecker 积AI 解读

Matrix differentiation, the procedure of finding partial derivatives of the elements of a matrix function with respect to the elements of the argument matrix, is the subject matter of this paper. The method followed here amounts to linking the differentials of the matrix function and the argument matrix, and then identifying matrices of partial derivatives. The basic assumption made is mathematical independence of the elements of the argument matrix. Matrix functions are…

Durbin–Watson 检验与 BLUS 检验的功效比较AI 解读

In an earlier paper [5] the authors compared the power of the BLUS test with the probability of a correct decision of the Durbin-Watson bounds test. A method to compute the distribution of the Von Neumann ratio under the null hypothesis and under the alternative hypothesis was given. In the present paper the latter method is used to tabulate the BLUS-test statistic and to compute the exact significance points of the Durbin-Watson test for several examples. Powers of both…

普通最小二乘与两阶段最小二乘估计量的精确抽样分布AI 解读

This paper presents the exact sampling distributions of the ordinary and the two-stage least squares estimators of a structural parameter in a structural equation with two endogenous variables in a complete system of stochastic equations. The results show that the distributions of the two estimators are essentially similar to each other. It can also be seen that both distributions depend crucially upon the deviation of a regression coefficient of disturbance terms of two…

正态总体样本双侧预测区间的计算因子AI 解读

Factors r(k, n; γ) for a normal distribution are given such that one may be 100γ% confident that the two-sided prediction interval will contain all of k future values, where and s are the sample mean and standard deviation from n previous observations. A special case is a prediction interval for a single future observation, which can also be obtained using percentage points of the Student t-distribution. Curves which indicate the extent to which two previously proposed…

有限总体乘积矩的进一步结果AI 解读

In a previous paper [4] an estimate of the 4-variate product moment was obtained. This estimate had a slight bias, as we pointed out. In this paper an unbiased estimate of the 4-variate product moment is obtained. Asymptotic results for the 3-variate and 4-variate product moments and their estimates are also obtained.

非抽样误差对2 × 2列联表关联度量的影响AI 解读

The effects of non-sampling errors on measures of association in 2 × 2 contingency tables are evaluated by the application of models due to the U. S. Bureau of the Census. This is achieved by first expressing the appropriate sample estimates in the form of Taylor series approximations involving cell probabilities, and then applying the model in a term by term fashion. In this way, the relative effects of sampling errors and response errors on the variability of an estimated…

每层仅抽取一个单位时的方差估计AI 解读

A new solution to the problem of variance estimation with one unit per stratum is presented. This method may lead to smaller bias in variance estimation, in many situations, than the methods of ‘collapsed strata’. It requires that we can associate with the strata concomitant variables which are correlated with the strata means. Several numerical examples with one or two concomitant variables are considered.

多阶段调查中的估计AI 解读

A superpopulation model is proposed for two-stage sampling from a finite population and we consider the problem of estimating a linear function of the finite population elements. We find the estimate with smallest mean squared error among linear estimates with bounded mean squared error without any assumption about the form of the super-population distribution. If the superpopulation is assumed to be normal this estimate is the mean of the posterior distribution. The…

检测供应商数据截断的超越检验AI 解读

The purpose of this paper is to present an easily applied test useful in determining whether or not a supplier's data have been truncated. The proposed test has the following desirable properties: (i) it is the uniformly most powerful rank test, (ii) it is asymptotically uniformly most powerful, (iii) power computations can easily be made for arbitrary sample sizes, formulas for such computations being given in the paper. Although formulated in the context of verifying a…

使用因子分析估计参数AI 解读

Factor analysis has been traditionally utilized for three broad purposes: First, as a data reduction technique which will hopefully simplify a multivariate situation to a smaller set of dimensions and enable the researcher to utilize data on a large number of variables; second, as an indexing device in which overtly manifested data are transformed to provide the latent or unobservable trait of a phenomenon; finally, as a cluster technique which helps the researcher to…

州生产总值与州级计量经济模型AI 解读

A methodology for estimating a state's gross state product (GSP) from primary data sources is presented and applied to Ohio. The social accounts for estimating GSP are used as a skeletal framework orf building a 27 equation econometric model of Ohio. The model is essentially an interdependent system consisting of behavioral equations in the following sectors: consumer, investment, state fiscal, output and personal income, and federal income tax. The sample period for most of…

建筑价格变化的测度AI 解读

The development of a statistically adequate set of construction price indexes is the goal of a research effort recently instituted at the Bureau of the Census. This paper describes research done to date on price indexes for single-family houses and indicates plans for future research. Using data from the Bureau's Housing Sales Survey, indexes of the price of new one-family houses sold (including value of site) have been computed by determining the most important…

健康研究中的统计推断问题：以吸烟与肺癌争议为例AI 解读

Disagreement about the role of cigarette smoking in lung cancer is traced to three sources of confusion. In the first, there is lack of agreement as to the definition of terms and what is implied when a specific factor is said to be a cause of a particular disease. A suggested definition is offered to clarify one of the issues causing dissent. The second area of disagreement concerns the method of measuring the strength of the relationship in a 2 × 2 table, and whether the…

摘要暂缺

平衡不完全区组设计中的方差分量估计量AI 解读

Estimation of variance components when the design is a balanced incomplete block, the model is additive, and error, block and treatment components are normal, independent, with zero expectations, is considered using variance as a criterion. The sections are arranged in the following manner: 1—The results are summarized. 2—The notation, model, statistics and analysis of variance tables are introduced. 3—A 1–1 (linear) transformation of the sufficient statistics is performed,…

受约束最小二乘估计量AI 解读

The method of Sweep-Out is used to obtain computing formulas for calculating the least-squares estimator and its variance matrix in linear models, not necessarily of full rank, in which certain restrictions may hold on the actual parameters. A test for a specified value of parametric restrictions is also discussed.