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判别分析中缺失值处理的渐近性质札记AI 解读

In an earlier article the authors studied five methods of handling missing values in discriminant analysis for small samples; this note points out the asymptotic behavior of these methods when the variables are equally correlated. The methods using either complete observation vectors or all sample values always attain the maximum probability of correct classification. Differences of the asymptotic probability of correct classification from its maximum are found to be small…

判别分析中缺失值处理的渐近性质札记AI 解读

In an earlier article the authors studied five methods of handling missing values in discriminant analysis for small samples; this note points out the asymptotic behavior of these methods when the variables are equally correlated. The methods using either complete observation vectors or all sample values always attain the maximum probability of correct classification. Differences of the asymptotic probability of correct classification from its maximum are found to be small…

协方差矩阵不等时的判别函数AI 解读

This study compares by Monte Carlo methods the performance of three discriminant functions in classifying individuals into two multivariate normally distributed populations when covariance matrices are unequal—the quadratic, best linear and Fisher's linear discriminant function. The comparison is carried out both asymptotically and using samples. The expected value of the probabilities is used as the measure of performance. Parameters that are varied in the study include the…

同一批个体上测得的相关系数AI 解读

When two correlation coefficients are calculated from a single sample, rather than from two samples, they are not statistically independent, and the usual methods for testing equality of the population correlation coefficients no longer apply. This paper considers the situation when the sample is from a multivariate normal distribution. Several possible large sample testing procedures are given, all based on Fisher's z-transformation. Power curves are given for each…

有限区间内回归直线置信带的一则说明AI 解读

In a recent article Graybill and Bowden give a method for constructing a confidence band for the entire regression line in simple linear regression. Each bound consists of two straight line segments rather than of the usual branch of a hyperbola. The method uses tables of the studentized maximum modulus with parameter m = 2 and d.f. = n − 2.The present note suggests a method for obtaining linear confidence bands designed to be used over a finite range rather than from − ∞ to…

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利用 t 分布估计多个对比AI 解读

Various methods based on Student t variates have been suggested and used for obtaining simultaneous confidence intervals for several means, or for several contrasts among means. Determination of an overall confidence level for such intervals involves evaluating the probability mass of a multivariate t distribution over a hypercube centered at the origin, with sides paralleling the coordinate planes, or obtaining bounds for this probability mass. Since such distributions…

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多个均值之间的多重比较AI 解读

Methods for constructing simultaneous confidence intervals for all possible linear contrasts among several means of normally distributed variables have been given by Scheffé and Tukey. In this paper the possibility is considered of picking in advance a number (say m) of linear contrasts among k means, and then estimating these m linear contrasts by confidence intervals based on a Student t statistic, in such a way that the overall confidence level for the m intervals is…

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基本统计方法AI 解读

Statistical analyses involving multiple predictors are generalizations of simpler techniques developed for investigating associations between outcomes and single predictors. Although many of these should be familiar from basic statistics courses, we review some of the key ideas and methods here as background for the methods covered in the rest of the book and to introduce some basic notationKeywordsCoronary Heart DiseaseSystolic Blood PressureOrdinary Little SquareSurvival…

相关正态变量均值的置信区间AI 解读

Several possible methods are presented for constructing confidence intervals for the means of normally distributed, dependent variables when nothing is known about the correlations. One, which uses the Student t distribution, is found, when the degrees of freedom is not too small compared to the number of variables, to give intervals almost as short as can possibly be attained. Methods based on Hotelling's T and on Scheffé's confidence intervals for all linear contrasts are…