论文标题
多项式错误模型中的预测
Prediction in polynomial errors-in-variables models
论文作者
论文摘要
考虑了具有截距项和多项式EIV模型的多元误差（EIV）模型。将重点放在结构同性恋情况下，在该案例中，协变量为I.I.D.测量错误是I.I.D.也是如此。被错误污染的协变量是正态分布的，并且还假定相应的经典错误是正常的。在这两个模型中，都表明（不一致的）回归参数的（不一致的最小二乘估计值）产生了A.S.鉴于可观察到的协变量的值，近似响应的最佳预测。因此，不仅在线性EIV中，而且在多项式EIV模型中，在预测问题中，回归参数的一致估计量毫无用处，前提是，预测受试者的观察误差的大小和协方差结构与模型拟合的数据中的数据没有差异。
A multivariate errors-in-variables (EIV) model with an intercept term, and a polynomial EIV model are considered. Focus is made on a structural homoskedastic case, where vectors of covariates are i.i.d. and measurement errors are i.i.d. as well. The covariates contaminated with errors are normally distributed and the corresponding classical errors are also assumed normal. In both models, it is shown that (inconsistent) ordinary least squares estimators of regression parameters yield an a.s. approximation to the best prediction of response given the values of observable covariates. Thus, not only in the linear EIV, but in the polynomial EIV models as well, consistent estimators of regression parameters are useless in the prediction problem, provided the size and covariance structure of observation errors for the predicted subject do not differ from those in the data used for the model fitting.
