Model selection, inference strategies and their applications

模型选择、推理策略及其应用

• 批准号: 98832-2011
• 负责人: Ahmed, SyedEjaz
• 金额: $ 2.04万
• 依托单位: Brock University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2014
• 资助国家: 加拿大
• 起止时间: 2014-01-01 至 2015-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=545105
• 关键词: Model; selection; inference; strategies; their

Ascertaining the appropriate statistical model-estimator for use in representing the data sampling process is an interesting and challenging problem in statistical research. In the main part of this proposal, we consider model selection and post model parameter estimation strategies in a host of scenarios and applications. Recent literature on variable selection focuses on using the data from an experiment to find a candidate subspace that represents a sparsity pattern in the predictor space. In the next round of experiments, researchers may consider this information and use either the full model or the candidate submodel. The strategy in this project is inspired by Stein's result that, in dimensions greater than two, efficient estimates can be obtained by shrinking full model estimates in the direction of submodel estimates. In some studies, many covariates are collected and included in the initial model. Because this may increase the uncertainty of the results, variable selection will be a crucial part of statistical analysis. Parsimony and reliability of predictors are desirable characteristics of statistical models. One possible source of prior information consists of knowing which of the predictor variables are of main interest and which variables are nuisance variables such as lab or age (candidate confounders) that may not affect the analysis of the association between the response and the main predictors. Another source of prior information is knowledge of results from previous experiments that search for sparsity patterns. This knowledge can be used to propose candidate subspaces. However, shrinking the full model estimator in the direction of the subspace leads to more efficient estimators when the shrinkage is adaptive and based on the estimated distance between the subspace and the full space estimators. We will establish risk properties of the shrinkage estimators via asymptotic distributional risk, a novel approach, and Monte Carlo experiments. It is expected that the proposed research will provide a unified strategy to researchers and practitioners for inference after variable selection and in assessing the predictive ability of the model at hand.

确定用于表示数据采样过程的适当统计模型估计器是统计研究中一个有趣且具有挑战性的问题。在本提案的主要部分中，我们考虑了许多场景和应用中的模型选择和模型后参数估计策略。最近有关变量选择的文献侧重于使用实验数据来查找表示预测变量空间中稀疏模式的候选子空间。在下一轮实验中，研究人员可能会考虑这些信息并使用完整模型或候选子模型。该项目中的策略受到 Stein 结果的启发，即在大于 2 的维度中，可以通过在子模型估计的方向上缩小完整模型估计来获得有效的估计。在一些研究中，收集了许多协变量并将其包含在初始模型中。由于这可能会增加结果的不确定性，因此变量选择将是统计分析的关键部分。预测变量的简约性和可靠性是统计模型的理想特征。先验信息的一个可能来源包括了解哪些预测变量是主要感兴趣的以及哪些变量是无用变量，例如实验室或年龄（候选混杂因素），这些变量可能不会影响响应与主要预测变量之间关联的分析。先验信息的另一个来源是先前搜索稀疏模式的实验的结果知识。该知识可用于提出候选子空间。然而，当收缩是自适应的并且基于子空间和全空间估计器之间的估计距离时，在子空间方向上收缩全模型估计器会导致更有效的估计器。我们将通过渐近分布风险、一种新颖的方法和蒙特卡罗实验来建立收缩估计器的风险属性。预计所提出的研究将为研究人员和从业者提供统一的策略，以便在变量选择后进行推理并评估现有模型的预测能力。