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:一种两阶段方法使研究者能够利用广义岭回归,基于包含两个及以上x预测变量的模型,在仅做出最小程度现实假设的条件下实现最优非线性预测。所得最优回归系数估计值在正态分布理论下或无偏,或最可能具有最小均方误差风险。所有必要计算与图形展示均通过当前版本的CRAN R语言程序包生成。本文以"修正后"的USArrests数据集作为数值案例,介绍并阐释了这一新型稳健统计方法。将这一策略应用于包含数百个观测值的回归模型虽直接可行,但此类情况下所需计算量可能相当庞大。