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经济时间序列缺失观测的最佳线性无偏估计AI 解读

The best linear unbiased estimator which we proposed previously for interpolating, distributing, and extrapolating a time series by related series is applied to the estimation of missing observations. Under special assumptions, the problem reduces to the one treated in Doran [2]. Our estimator is compared with his and is shown to be more efficient.

未知参数非线性计量经济系统的控制AI 解读

An approximate solution, based on the method of dynamic programming, is provided for the optimal control of a system of nonlinear structural equations in econometrics with unknown parameters using a quadratic loss function. It generalizes the methods previously proposed by the author for the control of a nonlinear econometric model with constant parameters and of a linear econometric model with uncertain parameters. It is an improvement over the method of certainty…

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基于贝叶斯方法的随机差分方程多期预测AI 解读

Given n observations on a system of linear stochastic difference equations with appropriate initial conditions, and given a prior density (possibly diffuse) of its parameters, this paper obtains the predictor of the time series k periods into the future with minimum mean squared error. Completely analytical solution is given for predictions from the first-order univariate system, and, in the general higher-order multivariate case, for k up to 5. econometric equations to…

计量经济学：统计基础与应用AI 解读

1. Elementary Aspects of Multivariate Analysis.- 1.1 Preliminaries.- 1.2 Joint, Marginal, and Conditional Distributions.- 1.3 A Mathematical Digression.- 1.4 The Multivariate Normal Distribution.- 1.5 Correlation Coefficients and Related Topics.- 1.6 Estimators of the Mean Vector and Covariance Matrix and their Distribution.- 1.7 Tests of Significance.- 2. Applications of Multivariate Analysis.- 2.1 Canonical Correlations and Canonical Variables.- 2.2 Principal Components.-…

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多元线性回归中最小二乘与向量相关的一个定理AI 解读

This paper shows that the least-squares estimate of the matrix of coefficients in a multivariate linear regression model maximizes the squared vector correlation coefficient between the dependent variables and a linear transformation of the explanatory variables.

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A natural generalization of least squares is proposed to estimate parameters in simultaneous linear equations. Full-information maximum likelihood is shown to be identical with this generalization. The extent to which other estimators deviate from the generalization is discussed. A paradox of Strotz is resolved, and application of canonical correlation theory to structural equations is indicated. 1. SUMMARY THIS PAPER compares various estimators of the parameters of linear…

两个线性回归中系数集合的相等性检验AI 解读

Having estimated a linear regression with p coefficients, one may wish to test whether m additional observations belong to the same regression. This paper presents systematically the tests involved, relates the prediction interval (for m = 1) and the analysis of covariance (for m > p) within the framework of general linear hypothesis (for any m), and extends the results to testing the equality between subsets of coefficients.