A Two-Stage approach enables researchers to make optimal non-linear predictions via Generalized Ridge Regression using models that contain two or more x-predictor variables and make only realistic minimal assumptions. The optimal regression coefficient estimates that result are either unbiased or most likely to have mininal MSE risk under Normal distribution theory. All necessary calculations and graphical displays are generated using current versions of CRAN R-packages. A numerical example using the "corrected" USArrests data.frame introduces and illustrates this new robust statistical methodology. While applying this strategy to regression models with several hundred observations is straight-forward, the computations required in such cases can be extensive.
翻译:两阶段方法使研究者能够利用包含两个或多个x预测变量的模型,通过广义岭回归做出最优非线性预测,且仅需做出现实的最小假设。由此得到的最优回归系数估计要么无偏,要么在正态分布理论下最可能具有最小均方误差风险。所有必要的计算和图形展示均使用当前版本的CRAN R包生成。通过使用"修正版"USArrests数据框的数值案例,介绍并阐明这一新的稳健统计方法。尽管将该策略应用于包含数百个观测值的回归模型是直接可行的,但此类情况下的计算量可能相当庞大。