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随机效应模型中的相关误差AI 解读

The usual one-way random model for the analysis of variance is broadened to allow for negative correlation between true residuals in the same row or cluster. This gives rise to an essential unidentifiability of parameters. Nonetheless, the likelihood function is typically such that the joint posterior distribution of all parameters is quite informative and there is enormous evidence for negative correlation whenever the sum of squares within is sufficiently large. Indeed, as…

经济系统计算机模拟实验中的实验设计问题AI 解读

Experimental design considerations have been virtually ignored by economists who have conducted computer simulation experiments with models of economic systems. The objective of this paper is to spell out in detail the relationship between existing experimental design techniques and techniques of data analysis and the design of simulation experiments with economic systems. We begin by defining the problem of experimental design as applied to computer simulation experiments.…

正态性假设下虚拟变量回归的渐近方差AI 解读

Asymptotic variances are derived for estimators of the dummy variate regression model described in [6]. The results are summarized by asymptotic covariance matrices for the regression coefficients, the estimated logarithms of odds given X, and the estimated probabilities given X. A two population two variable example illustrates the results.

普通最小二乘估计为最优线性无偏估计的充要条件AI 解读

It is shown that in a standard linear regression model ordinary least-squares estimators are best linear unbiased if and only if the errors have the same variance and the same nonnegative coefficient of correlation between each pair.

加权回归估计量的方差AI 解读

Formulas for the variances of weighted least squares estimators calculated with estimated weights based on equal replicate numbers are derived in this paper. Results are obtained for the two cases of multivariate and univariate error distributions.

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非中心卡方变量非中心参数的最大似然估计AI 解读

The maximum likelihood estimate for the non-centrality parameter of a non-central χ2 distribution with two degree of freedom is obtained. This estimate is expressed as a solution of an equation involving Bessel functions of order 0 and 1, of purely imaginary argument, both of which are tabulated. The derivation rests mainly on a lemma dealing with limit and monotonicity properties of a function representable as a quotient of two Bessel functions. An asymptotic result is also…

效率稳健的两样本秩检验AI 解读

In the classical two sample problem, the null hypothesis of identical distribution functions is tested. Rank testing procedures have the property that they are valid (have Type I error identically equal to α) for any absolutely continuous distribution function. Choices among rank tests are usually based upon local power calculations for a given specified null distribution against specific parametric alternatives. A rank test is said to be efficiency robust when no other has…

双向布局中的若干最优非参数程序AI 解读

Some optimum nonparametric procedures for estimating and testing contrasts in two-way layouts are proposed and studied. These procedures are based on the Chernoff-Savage [4] type of rank order statistics which include the Wilcoxon and normal scores statistics among others. In the first three sections, the properties of the proposed point estimators of contrasts, such as symmetry, invariance and asymptotic normality, are studied and their asymptotic relative efficiencies with…

基于秩的协方差分析AI 解读

Various methods are discussed for the problem of comparing two or more populations with respect to a response variable Y in the presence of a (possibly multivariate) concomitant variable X—a situation in which the usual method is the standard one-way analysis of covariance. A method based on ranks is developed.

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不平衡单向随机分类中随机效应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 one-way random classification where the number (Ni ) of observations in the ith class is treated as a random variable not necessarily independent of the class effect (Ai ). It is assumed that in general P(Ni = 0) > 0. The conditional expectations (given the number of observations in each class) of all estimators of the between variance component (σ2 a ) belonging to a certain class of…

正态假设下虚拟变量回归的渐近方差AI 解读

Asymptotic variances are derived for estimators of the dummy variate regression model described in [6]. The results are summarized by asymptotic covariance matrices for the regression coefficients, the estimated logarithms of odds given X, and the estimated probabilities given X. A two population two variable example illustrates the results.

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效率稳健的两样本秩检验AI 解读

In the classical two sample problem, the null hypothesis of identical distribution functions is tested. Rank testing procedures have the property that they are valid (have Type I error identically equal to α) for any absolutely continuous distribution function. Choices among rank tests are usually based upon local power calculations for a given specified null distribution against specific parametric alternatives. A rank test is said to be efficiency robust when no other has…

最优稳健性的一般方法及其在线性位置估计中的应用AI 解读

A general method of determining efficiency-robust estimation and testing methods is presented. This is used to derive admissible linear unbiased estimators (ALUEs) having the following optimality property: Over a specified (finite) family of possible symmetric shapes of the error distribution, the estimator's respective variances cannot be jointly improved. Such estimators are generalizations of Lloyd's best linear unbiased estimators (BLUEs) determined for single shapes.…

关于多元线性回归最小二乘法的一个定理AI 解读

This note shows that the least squares estimate of the matrix of coefficients in multivariate linear regression model maximizes all the sample canonical correlations between the dependent variables and the linear transformations of the explanatory variables, and it maximizes all the characteristic roots of the sample regression sum of squares and products matrix due to regression of the dependent variables on the linear transformations of the explanatory variables.

具有指定边际分布的多元分布构造说明AI 解读

A method for generating multivariate distributions with marginals in a prescribed family is introduced. It is a straightforward generalization of a method due to Marshall and Olkin.

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存在零差值时符号秩抽样分布的正态近似AI 解读

If, in using the Wilcoxon signed-rank test, the ranks corresponding to zero differences are deleted, the usual formula for the critical ratio used with the normal approximation must be modified. This note gives the required modification.

协变量不受控制时协方差分析的结构回归方法AI 解读

Analysis of covariance, with a single covariable in a randomized block design, is reconsidered in terms of structural regression. In practice, the covariable is often times uncontrolled, both in the experiment and in repeated sampling, and may follow a linear model as does the variable of interest. If the covariable is unaffected by treatments, then the covariable model may contain a block effect through no treatment effect. When such a model is adequate, the treatment…

误差空间的标准正交基及其在残差正态性和方差分析中的应用AI 解读

Under the assumptions of a linear model with independent residuals, the elements of an orthonormal basis of the corresponding error space can be used to construct normality tests, variance homogeneity tests, and variance estimators. In comparison with other available methods, this theoretically simple approach is more generally applicable, and also yields specific improvements in some particular cases. Some constructions and applications of orthonormal bases of error spaces…