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若干多元位置问题的非参数置信域AI 解读

Nonparametric methods of constructing confidence regions for the location vectors in the multivariate one-sample and two-sample problems are provided. These methods are based on a class of rank order statistics studied in detail by the authors in [8, 9, 11, 13]. Specifically, nonparametric confidence regions based on the Bonferroni inequality, the maximum modulus, and Scheffé's method are studied. The results obtained are nonparametric generalizations of some of the results…

结构系数估计量的精确分布AI 解读

The distribution studied is that of an estimator of a structural parameter appearing in a system of linear simultaneous equations. The relationship between the bias and the true parameter value is analysed and the bias is tabulated for selected values of the parameters of the distribution. It is also shown that the estimator possesses finite moments up to order v where v is the number of overidentifying restrictions and that the estimator converges to the true parameter…

似不相关回归不同估计量的小样本性质AI 解读

A Monte Carlo experiment is carried out to examine the small sample properties of five alternative estimators of a set of linear regression equations with mutually correlated disturbances. The estimators considered are ordinary least squares, Zellner's two-stage Aitken, Zellner's iterative Aitken, Telser's iterative, and maximum likelihood. The experiment, based on 100 samples, provides approximate sampling distributions for samples of size 10, 20 and 100 for various model…

股利政策的实证分析AI 解读

Starting with the “partial adjustment model” suggested by Lintner [10, 11], this paper examines the dividend policies of individual firms. The Lintner model, in which the change in dividends from year t-1 to year t is regressed on a constant, the level of dividends for t-1, and the level of profits for t, explains dividend changes for individual firms fairly well relative to other models tested. But a model in which the constant term is suppressed and the level of earnings…

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若干多元位置问题的非参数置信区域AI 解读

Nonparametric methods of constructing confidence regions for the location vectors in the multivariate one-sample and two-sample problems are provided. These methods are based on a class of rank order statistics studied in detail by the authors in [8, 9, 11, 13]. Specifically, nonparametric confidence regions based on the Bonferroni inequality, the maximum modulus, and Scheffé's method are studied. The results obtained are nonparametric generalizations of some of the results…

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双向完全随机分类中子类均值与观测数量的统计依赖AI 解读

This paper deals with certain aspects of variance-component estimation for the unbalanced two-way completely-random classification where the numbers of observations in the subclasses are treated as random variables not necessarily independent of some of the random effects of the model. General results are given on the expectations of two commonly-used estimators of the vector of variance components. Numerical approximations are presented for these expectations for one…

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规模显著变化时按规模比例概率重设计区域样本的方法AI 解读

For purposes of obtaining statistical data by enumeration, systematic sampling with probability proportional to size in one or more stages is frequently employed. The article describes two methods of changing the measures of sizes without introducing a bias in the estimation procedure. They result in the reduction of the variance of sample take, and, in the illustrative material presented, result in varying degrees of overlap before and after the changes of sizes. These…

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已知变异系数的正态分布均值估计札记AI 解读

The purpose of the present note is to find the best possible estimator of the parameter θ in the normal distribution N (θ, aθ2) (θ > 0) where α is a known positive constant. It is shown that neither the sample mean nor the sample standard deviation with suitably chosen constant is any longer the best unbiased estimator in the sense of minimum variance. Among a typical class of unbiased estimators, the one with minimum variance is obtained. It is also shown that the suggested…

关于对数线性回归的一则说明AI 解读

This paper presents a reparameterization of the conventional loglinear regression model. This reparameterization is shown to be more reasonable than the conventional specification. The stochastic assumptions of this reparameterized model are derived from the expected value properties of the dependent variable. Comparison with the conventional method of fitting log-linear models shows the regression intercept and the variance of the regression intercept to be different. A…

有限区间内回归直线置信带的一则说明AI 解读

In a recent article Graybill and Bowden give a method for constructing a confidence band for the entire regression line in simple linear regression. Each bound consists of two straight line segments rather than of the usual branch of a hyperbola. The method uses tables of the studentized maximum modulus with parameter m = 2 and d.f. = n − 2.The present note suggests a method for obtaining linear confidence bands designed to be used over a finite range rather than from − ∞ to…

自变量取值受限时线性回归的置信带AI 解读

Several writers have studied the problem of obtaining confidence bands for a straight line regression under the requirement that the bands be at a specified confidence level, (1 – α) say, for values of the independent variable restricted to a pre-specified closed interval. The bands studied by other writers have been either bands of equal width throughout the interval or trapezoidal bands. This paper studies confidence bands of the classical hyperbolic type under the…

双重非中心 t 分布的级数表示AI 解读

This paper gives analytic expressions for the distribution function of t″, a doubly noncentral t-distribution, with v degrees of freedom and noncentrality parameters δ and λ, in series of Incomplete Beta and Hypergeometric (Gauss and Confluent) functions. Numerical values of Pr(t″ ≤t| ν, δ, λ) for v = 2 (1) 20, λ = 0 (2) 8, |δ| = 0 (1) 5, t = 0 and 1 are given in Table I.

向区间收缩的均值估计与精度借用AI 解读

The topic of the shrinkage of an estimator for the mean of a normal distribution towards a point ([3] Thompson) is extended to shrinkage to an interval centered at μ = 0. An effort is made to keep the form of the modified estimator relatively simple, while obtaining more flexibility than is possessed by the sample mean . The family of estimators advocated is: Curves of MSE/σ (where MSE is mean square error) versus |μ/| are given for a number of values of θ and κ. A table is…

小而相等期望频数下卡方拟合优度检验功效近似的准确性AI 解读

This paper presents the results of a Monte Carlo study of the accuracy of an approximation to the power of the chi-square goodness of fit test with small but equal expected frequencies. Various combinations of sample size, number of groups, and alpha level are considered, and in most instances the actual power of the test is estimated to be less than the nominal power. The degree of accuracy appears to be more related to the size of the sample than to the size of the…

三变量分布中线性回归的一则札记AI 解读

Sufficient conditions that one marginal variable should be linearly regressed on the others are obtained for those trivariate distributions, generated by having additive random elements in common.

双非中心 t 分布表示的一则札记AI 解读

The first part of this note is devoted to some of the simpler series representations of the doubly non-central t-distribution. In the second part, the computational considerations arising from the series representations are discussed. A table showing some of the results of the method is presented.

嵌套抽样中的负方差估计与统计依赖AI 解读

Negative components of variance estimates may arise when the usual specification of statistically independent random variables is false. A class of such situations is considered here, viz., those in which the assumption of sampling from infinite populations is incorrect.

调查抽样中不等概率域估计量的使用AI 解读

Unbiased estimates of population parameters can be obtained from a sample survey when the sample units are not the primary units of estimation, i.e., when the correspondence between the units selected in the sample and the units of interest is not one to one. The survey technique used was that of a mail questionnaire with direct interviews of a subsample of non-respondents. The estimation technique used was that of domain estimators with unequal probability. Feasible…

利用先验信息进行分层与多阶段抽样的最优分配AI 解读

The author [1], [2] has given an algorithm for finding that stratified allocation which minimizes the posterior variance of the overall population mean subject to a budget constraint under a model in which a normal prior distribution and independent normal sampling distributions were assumed. The budget constraint assumed a variable per unit cost of observation. In the present paper these results are extended to cover the case where there are fixed costs, as well as variable…