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论一种受约束最小二乘估计量
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.
受约束最小二乘估计量
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.
单因素分类中协方差分析的稳健性
SUMMARY The effect of non-normality and the effect of treatment slope interaction in the analysis of covariance is studied. Unlike the analysis of variance F-test the analysis of covariance F-test is found to be appreciably affected by non-normality even in balanced classifications. The degree of sensitivity to non-normality is determined by the distribution of the concomitant variables. The violation of the assumption of no treatment-slope interaction does not seem to have…
非正态性对方差分量估计的影响
SUMMARY The effect of non-normality in estimating variance components in a random effects or mixed effects linear model is studied. It is shown that for a wide variety of balanced situations the interval estimation of the upper variance component is likely to be relatively little affected by non-normality in the error component. A method is suggested for constructing a confidence interval for a ratio of variance components in a balanced model, without assuming normality.
二次平衡最小二乘问题中的残差方差估计与 F 检验的稳健性
In the first part of the paper a new simple proof is given of a special case of a result due to Hsu (1938) concerning the estimation of residual variance in a linear least-squares model. In the second part of the paper similar methods are applied to examine the effect of non-normality in the standard analysis of variance F -test. A condition is found for the test to be insensitive to non-normality; the condition is satisfied in the standard set-ups, such as balanced two-or…