Iterative Estimation of a Set of Linear Regression Equations
一组线性回归方程的迭代估计AI 解读 ↓
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一组线性回归方程的迭代估计
- 研究问题
- 当多条线性回归方程的扰动相关时，如何通过迭代利用跨方程信息，并比较其与逐方程最小二乘的渐近效率？
- 方法与思路
- 作者在解释变量非随机的设定下采用 Gauss–Seidel 递归估计，利用扰动相关，并讨论原回归与残差回归系数的估计。
- 材料陈述的贡献
- 摘要称各轮迭代估计渐近正态，迭代极限与 Zellner 广义最小二乘具有相同渐近分布；满足所述条件时可提高渐近效率。
- 阅读关注点
- 应核对跨方程扰动结构、解释变量或观测不同的条件，并区分样本量趋大与迭代次数趋大时的结论及残差估计作用。
- 阅读边界
- 仅据 OpenAlex 索引摘要，稿件版本未注明，不能判断刊本变化；摘要未给出完整正则条件、有限样本收益或数值收敛细节。
原文摘要
This article develops a method of calculating iterative estimates of the coefficients of a set of linear regression equations. There are p equations such that the explanatory variables are non-stochastic and it is assumed that the random disturbances of at least one pair of equations are correlated. Provided that either different explanatory variables enter the various equations or that if the same explanatory variables enter then the observations are different, it is possible to obtain estimators that are asymptotically more efficient than the simple one-at-a-time least squares estimators. The estimators developed herein are calculated recursively using the Gauss-Seidel method of iteration. It is shown that all of the iterations are asymptotically normal, and that in the limit the iterations have the same asymptotic distribution as the generalized least squares estimator proposed by Zellner. The iterative estimators directly exploit the correlations among the random disturbances. In addition p linear regression equations are defined such that in the ith equation the dependent variable is the residual of the original ith equation and the p − 1 “explanatory” variables are the residuals of all other regressions. It is shown that the regression coefficients of these residuals can be estimated recursively, jointly with the original regression coefficients, or directly from the one-at-a-time least squares residuals. All of these estimators of the regression coefficients of the random disturbances converge in distribution to the same multivariate normal law.