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正态总体分位数的置信带AI 解读

Given the general linear regression model , where y is N X 1, X of full rank is N X (q + 1), is (q + 1) X 1, and e is N(0, σ2I), Steinhorst and Bowden [5], using the theory of Roy's maximum root test statistics, set confidence bands for , of the normal population with mean and variance σ2, k being the pth quantile of the standard normal distribution, I fixed or specified but unknown and p known. However, narrower bands may be obtained using the exact test statistic,…

正态总体分位数的置信带AI 解读

Given the general linear regression model , where y is N X 1, X of full rank is N X (q + 1), is (q + 1) X 1, and e is N(0, σ2I), Steinhorst and Bowden [5], using the theory of Roy's maximum root test statistics, set confidence bands for , of the normal population with mean and variance σ2, k being the pth quantile of the standard normal distribution, I fixed or specified but unknown and p known. However, narrower bands may be obtained using the exact test statistic,…

正态线性回归系数的线性组合AI 解读

Summary In the literature the double linear compounds of the multivariate linear normal regression coefficients are tested by using Roy's maximum root test, see, for example, Khatri (1962) and Morrison (1967, p. 109, equation (13)). The test statistic is Student's t. The t statistic gives narrower confidence bounds than those given by Roy's maximum root statistic. Morrison uses Hotelling's T2 statistic for testing linear compounds of the mean vector. However, the exact test…

基于部分观测的样本均值与协方差多元预测区间AI 解读

By using the information provided by the first κ, 2 ≤ κ < N, members of a random sample of size N from a univariate normal distribution, Hickman [3] obtains prediction intervals for the sample mean, and the sample variance of the complete sample of size N. He gives similar results for a univariate normal regression model. Here we present straightforward generalizations of Hickman's results to the multivariate case.

基于部分观测的样本均值与协方差多元预测区间AI 解读

By using the information provided by the first κ, 2 ≤ κ < N, members of a random sample of size N from a univariate normal distribution, Hickman [3] obtains prediction intervals for the sample mean, and the sample variance of the complete sample of size N. He gives similar results for a univariate normal regression model. Here we present straightforward generalizations of Hickman's results to the multivariate case.

典型三方程情形中GCL估计量的精确分布AI 解读

Basmann [4] has recently obtained some results of the exact sampling distributions of the generalized classical linear (GCL) estimators of the parameters of a system of three simultaneous structural linear equations These results appear as generalizations of earlier results given by Basmann [5] for a system of two equations. Kabe [9] used the known properties of the noncentral Wishart distribution to give an alternative derivation of Basmann's results for the two-equation…

典型三方程情形下 GCL 估计量的精确分布AI 解读

Basmann [4] has recently obtained some results of the exact sampling distributions of the generalized classical linear (GCL) estimators of the parameters of a system of three simultaneous structural linear equations These results appear as generalizations of earlier results given by Basmann [5] for a system of two equations. Kabe [9] used the known properties of the noncentral Wishart distribution to give an alternative derivation of Basmann's results for the two-equation…

关于Wishart矩阵Bartlett分解的一则札记AI 解读

Summary By suitably factorizing the generalized variance, a concise derivation of the Bartlett decomposition of a central Wishart matrix is given. The method is extended to give a decomposition of a p-dimensional non-central Wishart matrix of rank t (≤ p), in terms of a t-dimensional non-central Wishart matrix of rank t, (p - t) independent χ2 variates and 1/2(p - t)(p + t - 1) independent unit normal variates.

逐步多元线性回归AI 解读

Freund, Vail, and Ross [2], Goldberger and Jochems [3], and Goldberger [4] have given some results for the stepwise estimation of the parameters of a univariate regression model. We give here similar results for a multivariate linear regression model.

多元线性回归的逐步估计AI 解读

Freund, Vail, and Ross [2], Goldberger and Jochems [3], and Goldberger [4] have given some results for the stepwise estimation of the parameters of a univariate regression model. We give here similar results for a multivariate linear regression model.

带线性约束的多元线性假设检验AI 解读

SUMMARY In this paper we consider a normal multivariate linear regression model and give a criterion for the simultaneous testing of a set of linear estimable parametric functions. We also derive the distribution of the criterion and obtain some allied results.

两个主要过度识别情形下GCL估计量精确分布的说明AI 解读

Basmann [3] has recently given the exact sampling distributions of the generalized classical linear (GCL) estimators of the parameters of a system of two simultaneous structural equations. In view of the importance of the GCL estimators in econometric statistics, a less intricate derivation by using formulae that might be more widely known to statisticians and econometricians, might be useful.

多元回归增删变量的Cochran公式推广AI 解读

By using Schweinsian expansion of determinant quotients, a concise derivation of Cochran's formulae for addition or omission of a variate in Multiple Regression Analysis is given. The formulae are extended to the case when two variates are simultaneously added or omitted. The addition or omission of more than two variates follows on similar lines. Schweinsian expansion has been earlier used by Cox [3] to derive the general orthogonal polynomials.

两类典型过度识别情形中 GCL 估计量精确分布的注记AI 解读

Basmann [3] has recently given the exact sampling distributions of the generalized classical linear (GCL) estimators of the parameters of a system of two simultaneous structural equations. In view of the importance of the GCL estimators in econometric statistics, a less intricate derivation by using formulae that might be more widely known to statisticians and econometricians, might be useful.

多元回归中增删变量的Cochran公式扩展AI 解读

By using Schweinsian expansion of determinant quotients, a concise derivation of Cochran's formulae for addition or omission of a variate in Multiple Regression Analysis is given. The formulae are extended to the case when two variates are simultaneously added or omitted. The addition or omission of more than two variates follows on similar lines. Schweinsian expansion has been earlier used by Cox [3] to derive the general orthogonal polynomials.