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线性过程误差回归中 GLSE 与 MLE 的二阶风险结构AI 解读

In a regression model with an error that is a general linear process, the second-order expansion of the risk matrix of GLSE or MLE is obtained. a set of sufficient conditions for the effect of estimating the structural parameter of the linear process to vanish in the above expasion is obtained. The relation of the covariance matrix of SLSE with those of GLSE and MLE up to $O(T^-2)$ is elucidated.

广义最小二乘估计量风险上界的一种方法AI 解读

First, an approach to an upper bound for the risk matrix of GLSE's is established when the information on the parameter space of the structural parameter in the covariance matrix of the error can be utilized. Second, this result is applied to regression with (i) serial correlation and (ii) heteroscedastic covariance structure. In the heteroscedastic regression, the problem of estimating the common mean of two normal populations is studied in detail.

参数经过估计的线性模型预测误差AI 解读

An expansion is obtained for the prediction mean squared error of the predictor with estimated parameters for the general statistical linear model. The samples and the estimators for the structural parameters contained in the variance-covariance matrix are assumed independent.

协方差参数经估计时广义最小二乘估计量均方误差矩阵的二阶展开AI 解读

The second-order expansion of the mean squared error matrix of the generalized least squares estimators for the regression parameters is obtained when the samples and the estimators for the structural parameters contained in the variance-covariance matrix are independent.

参数经估计的线性模型中的预测误差AI 解读

An expansion is obtained for the prediction mean squared error of the predictor with estimated parameters for the general statistical linear model. The samples and the estimators for the structural parameters contained in the variance-covariance matrix are assumed independent.

含估计参数的广义最小二乘估计量均方误差矩阵的二阶展开AI 解读

The second-order expansion of the mean squared error matrix of the generalized least squares estimators for the regression parameters is obtained when the samples and the estimators for the structural parameters contained in the variance-covariance matrix are independent.