Stability, Inference, and Weighting in Model Selection

三个组成部分的第一个建议的研究利用加权最小二乘估计的形式，开发新的方法回归诊断，鲁棒估计和变量选择。 第二部分解决了模型平均后的频率论推断问题，特别是“装袋”问题。提出了一种新的“平行引导”的回归方法，用于寻找方差估计的总计算工作量约为原来的装袋步骤的两倍。第三个组成部分解决了确定模型平均何时有益的问题。 模型平均通常会改善基础程序的预测，但并不总是如此。由于预测的改善是以牺牲可解释性为代价的，因此了解模型平均何时有利，何时不利是很重要的。因此，将开发和研究适用于一般回归模型的模型稳定性指数。拟议的研究解决了在估计因变量Y和几个预测变量之间的关系时出现的公认问题，例如，Y =贷款失败和X1 =家庭收入，X2 =受抚养人的数量等，本研究开发的方法和见解将是非常有用的回归建模的应用，从而将促进研究在许多其他学科，包括基础科学研究和应用研究，直接影响生活质量。结果将通过网络和期刊出版物、会议和研讨会传播。该项目还将以研究生教育和培训的名义对人力资源开发产生重大影响，鉴于北卡罗来纳州统计局对多样化研究生课程的承诺，其中一些人可能来自代表性不足的群体。

The first of three components to the proposed research exploits the form of weighted least squares estimators to develop new approaches to regression diagnostics, robust estimation, and variable selection. The second component addresses the problem of frequentist inference after model averaging, and "bagging" in particular. A new "parallel bootstrap" resampling approach is proposed for finding variance estimators with total computational effort about twice that of the original bagging step. The third component addresses the problem of determining when model averaging is beneficial. Model averaging often improves prediction over a base procedure, but not always. Because the improvement in prediction is achieved at the expense of interpretability, it is important to know when model averaging is advantageous and when it is not. Thus a model-stability index that is applicable to general regression models will be developed and studied.The proposed research addresses well-recognized problems that arise when estimating the relationship between a dependent response variable Y and several predictor variables, e.g., Y = loan failure and X1 = household income, X2 = number of dependents, etc. The methods and insights developed by this research will be very useful in applications of regression modeling and thus will facilitate research in numerous other disciplines including basic science research and applied research that directly affects quality of life. Results will be disseminated via web and journal publications, conferences, and seminars. The project will also significantly impact human resource development in the guise of education and training of graduate students, some of whom who are likely to come from under-represented groups in light of the NC State Statistics Department's commitment to a diverse graduate program.