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回归分析中的第二类模型AI 解读

Summary Regression models of the first and second kind are distinguished by the absence or presence, respectively, of variable regression coefficients. A characteristic of a model of the second kind is its heteroscedasticity. The problems of estimation in a general regression model of the second kind are discussed briefly. A more detailed examination is given of the properties of various estimators of the coefficients in the overall regression and scedastic curves for the…

Cobb–Douglas 生产函数中的边际产出估计AI 解读

The sampling properties of the usual estimator of marginal product from a CobbDouglas production function are studied under the assumption of normally distributed errors. The asymptotic normality of these estimators is demonstrated and certain special cases are considered for which the asymptotic distribution is particularly simple. An alternative estimator of marginal product is suggested which has both a smaller bias and greater precision than the usual estimator.…

截断分组双曲正割平方分布的位置与尺度参数估计AI 解读

The iterative calculations required to obtain the maximum likelihood estimates of α and β in the distribution function dF(z) = e z /(1 + e z )2 dz, where z = α +βx, are presented for doubly truncated, upper and lower truncated, and untruncated grouped samples. The calculations needed to obtain the maximum likelihood estimator of Pareto's constant are also given for a lower truncated grouped sample with both equal and unequal grouping. Asymptotic variances and covariances are…