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重新定位反向回归AI 解读

I am not sure that the imperfect correlation between workers' productivity and their measured qualifications creates, as Conway and Roberts suggest, a profound dilemma for the theory of distributive justice. On the other hand, I am fairly sure that it raises issues of statistical inference. And I am quite sure that statisticians are better equipped to resolve the latter than the former. So I will consider the choice of regression for inferring salary discrimination in the…

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单一潜变量的多指标多原因模型估计AI 解读

We consider a model in which one observes multiple indicators and multiple causes of a single latent variable. In terms of the multivariate regression of the indicators on the causes, the model implies restrictions of two types: (i) the regression coefficient matrix has rank one, (ii) the residual variance-covariance matrix satisfies a factor analysis model with one common factor. The first type of restriction is familiar to econometricians and the second to…

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利用分组观测估计帕累托定律AI 解读

The problem of estimating the scale parameter in the Pareto distribution from grouped observations is considered. Several estimators—the maximum likelihood estimator and four variants of least squares—are evaluated. Most of these have identical BAN properties but require nonlinear computations. A linearized BAN estimator is constructed, and numerical illustrations are provided.

随机变量乘积的精确协方差AI 解读

For the general case of jointly distributed random variables x and y, Goodman [3] derives the exact variance of the product xy. For the special case where x and y are stochastically independent, he provides a simpler expression for the exact variance. We offer a weaker set of assumptions which suffices to yield the simpler expression. We then extend Goodman's analysis to present the exact covariance of two products xy and uv, and sketch several specializations and…

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广义线性回归模型中的最佳线性无偏预测AI 解读

When interdependence of disturbances is present in a regression model, the pattern of sample residuals contains information which is useful in prediction of post-sample drawings. This information, which is often overlooked, is exploited in the best linear unbiased predictor derived here. The gain in efficiency associated with using this predictor instead of the usual expected value estimator may be substantial.

分步最小二乘：残差分析与设定误差AI 解读

A stepwise procedure for estimating the parameters of the multiple linear regression model y = X 1β1 + X 2β2 + e is often used. Two articles in the March 1961 issue of this Journal focussed on the connection between the stepwise and the direct estimator of β2. The present paper spells out the connection between the stepwise and the direct estimator of β1, as a special case of Theil's analysis of specification error. A unified treatment of the two stepwise estimators is also…

分步最小二乘简注AI 解读

A stepwise procedure is often used to estimate one coefficient in a multiple linear regression. The relation between this stepwise estimate and the estimate obtained by direct multiple regression is spelled out.

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