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关于方差合并估计的一个说明AI 解读

The estimation of variance in the normal distribution is studied under statistical inference based on conditional specification. When there are two samples available for estimating the variance and it is not certain whether the two samples are from the same population, the experimenter usually uses a test to resolve the uncertainty. When the test is not significant, the samples are pooled to obtain a pooled estimator; otherwise, the individual sample variance is used. The…

关于方差合并估计的一个注记AI 解读

The estimation of variance in the normal distribution is studied under statistical inference based on conditional specification. When there are two samples available for estimating the variance and it is not certain whether the two samples are from the same population, the experimenter usually uses a test to resolve the uncertainty. When the test is not significant, the samples are pooled to obtain a pooled estimator; otherwise, the individual sample variance is used. The…

摘要暂缺

基于二元与连续变量的判别分析AI 解读

An observation consisting of both binary and continuous variables may be classified into one of two populations by the double-discriminant function based on the point-biserial model. When the parameters are unknown or partially known, a sample double-discriminant function is obtained by replacing the unknown parameters by their sample estimates. A sampling scheme referred to as the double inverse sampling is proposed to ensure nonsingularity of the sample covariance…

基于二元与连续变量的判别分析AI 解读

An observation consisting of both binary and continuous variables may be classified into one of two populations by the double-discriminant function based on the point-biserial model. When the parameters are unknown or partially known, a sample double-discriminant function is obtained by replacing the unknown parameters by their sample estimates. A sampling scheme referred to as the double inverse sampling is proposed to ensure nonsingularity of the sample covariance…

摘要暂缺

方差分量的非负估计与预检验估计AI 解读

Nonnegative estimators of variance components involving preliminary tests are studied. The restricted maximum likelihood estimator and other truncated estimators may be viewed as preliminary test estimators. A new preliminary test estimator is proposed and studied. Recommendations of the levels of preliminary tests are made.

方差分量的非负估计量与预检验估计量AI 解读

Nonnegative estimators of variance components involving preliminary tests are studied. The restricted maximum likelihood estimator and other truncated estimators may be viewed as preliminary test estimators. A new preliminary test estimator is proposed and studied. Recommendations of the levels of preliminary tests are made.

线性判别分类后一组观测的总体均值估计AI 解读

Suppose that a group of observations is known to have come from either one of two normal populations with unknown means and common variance. After the group is classified by the linear discriminant function, it is pooled with the sample from the population to which it belongs to estimate the unknown mean. Weighted estimators of the population means are defined. The biases and mean squared errors of the estimators in the univariate case are obtained. Estimators of the…

线性判别分类后一组观测下的均值估计AI 解读

Suppose that a group of observations is known to have come from either one of two normal populations with unknown means and common variance. After the group is classified by the linear discriminant function, it is pooled with the sample from the population to which it belongs to estimate the unknown mean. Weighted estimators of the population means are defined. The biases and mean squared errors of the estimators in the univariate case are obtained. Estimators of the…

不完全指定固定模型中方差分析检验的水平与功效AI 解读

Derivations are given of the size and power of a test of a hypothesis for an incompletely specified fixed linear model. Such a testing procedure involves a test of a hypothesis of main interest subsequent to a preliminary test to determine the inclusion or not of a term in the tentatively specified complete fixed linear model. An evaluation of the formulas of the size and power was made over a wide range of values of the parameters involved, and recommendations concerning…

非中心卡方分布与正态分布的若干关系AI 解读

Cumulative distribution functions of noncentral ohi-squared distributions with odd degrees of freedom are expressed as functions of the distribution function and probability density function of the standard normal distribution. From these relationships, the probabilities can be easily computed. Some key words: Noncentral chi-squared distribution; Normal distribution. 1.

辅助变量信息不完整时的双重抽样AI 解读

It is well known that the precision of an estimator can be improved if auxiliary variables are used. In particular, if the relationship is linear, a linear regression estimator is constructed. When the mean of the auxiliary variable is completely unknown, double sampling techniques can be adopted. If the experimenter has partial information about the mean, he may perform a preliminary test and construct a preliminary test estimator. The bias, mean square error and relative…

协方差矩阵不相等情形下的判别分析札记AI 解读

A discriminant function is derived in the case of unequal mean vectors and unequal covariance matrices in two multivariate normal populations. The variates are assumed equally correlated. The discriminant function depends on the size and the shape components and the component of sum of squares of the variates.

一组相关变量的方差齐性检验AI 解读

To test the equality of a set of p variancas when the p variates are correlated with common correlation coefficient, four test procedures are proposed in this paper, namely, the asymptotic test, the modified Bartlett test, the multiple correlation test and the Fmax test. Comparisons among these four tests were made. A Monte Carlo study showed that, when p = 3, the sample size needed is about 40 in order that the asymptotic theory holds, while for p = 4 it needs about 50.

协方差矩阵不等时的判别分析注记AI 解读

A discriminant function is derived in the case of unequal mean vectors and unequal covariance matrices in two multivariate normal populations. The variates are assumed equally correlated. The discriminant function depends on the size and the shape components and the component of sum of squares of the variates.

一组相关变量的方差齐性检验AI 解读

To test the equality of a set of p variancas when the p variates are correlated with common correlation coefficient, four test procedures are proposed in this paper, namely, the asymptotic test, the modified Bartlett test, the multiple correlation test and the Fmax test. Comparisons among these four tests were made. A Monte Carlo study showed that, when p = 3, the sample size needed is about 40 in order that the asymptotic theory holds, while for p = 4 it needs about 50.