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条件正态回归模型AI 解读

A relatively complete discussion is provided for the limiting distributions of certain sample correlation coefficients and sample correlation ratios. It is assumed for the random variables X and Y that the conditional distribution of Y, given X = x, is multivariate normal with a constant, but unknown, covariance matrix and that the distribution of X has finite fourth moments. The sample coefficients are then based on a random sample from the (X, Y)-distribution. For the case…

一个变量被二分化时多元正态分布的参数估计AI 解读

The problem discussed is the estimation of the parameters of a multivariate normal distribution using a sample from a dichotomization of this distribution, with the emphasis on large-sample distributions of the estimators. The usual Newton's method is adapted to the present situation for the solution of the likelihood equations. The various expressions which are derived are illustrated by a problem in educational testing. Results extend those of Maritz (1953) and Tate (1955).

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正态分布方差的最优置信区间AI 解读

Tables of divisors of the sample sums of squared deviations from the mean are provided to yield either the confidence interval of minimum length or the “shortest” unbiased interval for the variance of a normal distribution. Some questions are raised concerning confidence intervals of minimum length.