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方差非负线性组合的置信区间AI 解读

Smith (1936) suggested a method that can be used for setting confidence limits on linear combinations of variances. This method was studied and expanded by Satterthwaite (1941, 1946) and has become known as Satterthwaite's procedure. The procedure has been widely used for the past 40 years. In this article a new procedure is proposed for this problem that is better than Satterthwaite's procedure and very easy to compute from existing tables.

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两因素嵌套方差分量模型中变异占比的置信区间AI 解读

In the two-factor nested variance component model with equal numbers in the cells given by y ijk = μ + A i + B ij + C ijk , three important functions of the variance components σA 2, σB 2, and σC 2 are the proportions of the total variation due to factors A, B, and C, which are given by σA 2/(σA 2 + σB 2 + σC 2), σB 2/(σA 2 + σB 2 + σC 2) and σC 2/(σA 2 + σB 2 + σC 2), respectively. There are no exact confidence intervals available for these proportions. In this article…

含交互作用的双向分类模型中误差方差的估计AI 解读

A method is given for estimating the error variance σ2 in a two-way classification model with interaction and with exactly one observation per cell. The method can also be used to help determine the pattern of interaction.

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简单线性模型的线段置信带AI 解读

In this paper confidence bands are given for the entire line for simple linear regressions. The conventional bands that have been given in the past are curvilinear. In this paper we consider confidence bands that are straight lines. It is shown that under certain conditions the “width” of these straight line bands is less than the width of the conventional curvilinear bands.

线性模型中等宽与比例宽度的置信带AI 解读

In this paper confidence bands are given for simple linear models. The confidence bands that are given are straight lines rather than curves and are either (1) parallel or (2) trapezoidal. The confidence bands are over a finite length interval.

双向分类混合模型设计的最小充分统计量AI 解读

This paper presents theorems which can be used to obtain sufficient and minimal sufficient statistics for the two-way classification mixed model design. Using the general linear hypothesis model Y=X τ+Z β+e the authors prove that the dimension of a minimal sufficient statistic is a function of the ranks of certain submatrices of Z×X. Minimal sufficient statistics are presented in tabular form for some two-way classification designs and some of the distributional properties…

双向分类混合模型设计的最小充分统计量AI 解读

This paper presents theorems which can be used to obtain sufficient and minimal sufficient statistics for the two-way classification mixed model design. Using the general linear hypothesis model Y=X τ+Z β+e the authors prove that the dimension of a minimal sufficient statistic is a function of the ranks of certain submatrices of Z×X. Minimal sufficient statistics are presented in tabular form for some two-way classification designs and some of the distributional properties…

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