New Approaches to Variable Selection

在这个项目中，研究人员将开发两种新的但相关的回归模型变量选择方法。这两个程序都使用多个蒙特卡罗生成的伪数据集来调整标准变量选择例程中的控制参数α(例如，α=正向选择中的“α-to-Enter”)。在第一种方法中，将白噪声加到响应变量中，并以全模型均方误差(FMMSE)的受控倍数m表示方差。对噪声增强的数据运行变量选择过程，并且为选择过程调整参数α的每个值找到所选择的模型均方误差(MSE)。对许多自举类型的复制重复该过程，并为每个m值保留平均均方误差。最优α被确定为对于噪声增强的数据平均给出理论上预期的均方误差FMMSE(1+m)的值。该方法对加性误差回归模型的变量选择过程具有广泛的适用性。在第二种方法中，将伪预测器添加到数据集，并且对于选择过程调整参数的不同值，估计包括在所选模型中的伪变量的比例。然后，通过对自举类型的复制进行平均，可以为工艺调整参数α的每个值的观测数据估计工艺的错误选择率(FSR)。FSR由Alpha选项控制。FSR是一个非常可以理解和有意义的数量来控制。这种方法不受加性误差模型的限制，因此比上述的噪声增强方法具有更广泛的适用性。回归建模是最广泛使用的统计方法。统计学家早就知道，回归模型中预测变量的选择是回归分析中最重要的组成部分。然而，重要预测变量的识别仍然是统计推断中最不被理解和最重要的公开问题之一。这适用于具有少数潜在预测变量的小型到中等数据集，以及具有数以千计的潜在预测变量的巨型数据集，这些数据集在统计应用中变得越来越普遍。在这个项目中，研究人员开发了从一组更大的潜在预测变量中识别重要预测变量的方法。研究的影响和回归建模的应用一样广泛。新方法将使所有应用领域的研究人员能够更好地使回归模型适应大大小小的数据集。应用的范围很广，例如包括基因微阵列数据、药物开发数据、人口普查局数据、信用卡交易或贷款申请等金融数据、大型天气和环境数据集以及电力使用数据。

In this project the investigators will develop two novel, but related,approaches to regression model variable selection. Both proceduresmake use of multiple, Monte Carlo-generated, pseudo data sets to tunethe controlling parameter alpha in a standard variable-selectionroutine (e.g., alpha = "alpha-to-enter" in forward selection). In thefirst approach, white noise is added to the response variable withvariance in controlled multiples, m, of the full-model mean squarederror (FMMSE). The variable selection process is run on thenoise-enhanced data, and the selected model mean squared error (MSE)is found for each value of the selection process tuning parameteralpha. This process is repeated for many bootstrap-type replicationsand the average MSE is retained for each value of m. The optimal alphais determined as the value that gives, on average, the theoreticallyexpected mean squared error, FMMSE(1 + m), for the noise-enhanceddata. This approach has wide applicability to variable selectionprocedures used with additive-error regression models. In the secondapproach phony predictors are added to the data set, and theproportion of phony variables included in the selected model fordifferent values of the selection process tuning parameter isestimated. Then, by averaging over bootstrap-type replications, thefalse selection rate (FSR) for the process can be estimated for theobserved data for each value of the process tuning parameteralpha. The FSR is controlled by choice of alpha. The FSR is a veryunderstandable and meaningful quantity to control. This method is notrestricted to additive-error models and thus has wider applicabilitythan the noise-enhancement above.Regression modeling is the most widely used statistical procedure.Statisticians have long known that the choice of predictor variablesto use in a regression model is the most important component ofregression analysis. Yet the identification of important predictorvariables remains one of the least understood and most important openproblems in statistical inference. This is true for small to moderatedata sets with a handful of potential predictor variables, as well asfor the huge data sets with potential predictors numbering in thethousands that are becoming more prevalent in statisticalapplications. In this project the investigators develop methods foridentifying important predictor variables from a larger set ofpotential predictors. The impact of the research is as broad as theapplication of regression modeling. The new methods will enableresearchers in all application fields to better fit regression modelsto data sets, both small and large. The range of applications isenormous and includes, for example, genetic microarray data, drugdevelopment data, census bureau data, financial data such as creditcard transactions or loan applications, large weather andenvironmental data sets, and electric power usage data.