Collaborative Research: Higher-Order Asymptotics and Accurate Inference for Post-Selection

合作研究：高阶渐进和后选择的精确推理

基本信息

批准号：
1712940
负责人：
Todd Kuffner
金额：
$ 8万
依托单位：
Washington University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2017
资助国家：
美国
起止时间：
2017-08-01 至 2021-07-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1712940&HistoricalAwards=false
关键词：
Collaborative Research Higher Order Asymptotics

项目摘要

Many statistical analyses utilize a model selection procedure. Perhaps the most common model selection problem is that of variable selection in linear regression. Principled motivations for selection include the desire for interpretability, prevention of over-fitting, and concerns about statistical power. A practical motivation arises when the data are high-dimensional, with more explanatory variables than observations. Relevant applications span the entire domain of scientific inquiry, from neuroscience, medicine and physics, to economics, sociology, and psychology. A large catalogue of variable selection procedures is now available, and the statistics community has turned its focus to the question of inference after selection. Standard methods of statistical inference are no longer valid when the same data are used to both select a model and make inferences about that model. It is fundamentally important to have accurate post-selection inference procedures that are also powerful enough to detect observed departures from scientific hypotheses and that avoid the strong distributional assumptions needed for exact inference in finite samples. This research aims to develop post-selection inference methodology that is both accurate and powerful, with particular emphasis on reducing statistical errors that depend on the sample size. The goal of this project is to further understanding of the asymptotic theory of post-selection inference, particularly selective inference based on the CovTest and truncated Gaussian (TG) statistic, as well as simultaneous inference using the post-selection intervals (PoSI) procedure. The first two procedures can be motivated by selective error control, i.e., error control for the selected model parameters. The PoSI method seeks to control family-wise error rates for all possible sub-model parameters. While these procedures yield valid post-selection inference, without strong assumptions they are particularly vulnerable to the effects of violation of key assumptions in the realistic setting of small to moderate sample sizes, such as overly-conservative or inaccurate confidence intervals, and low power. In this project, asymptotic expansions, saddle-point approximations, the bootstrap, and related techniques from higher-order asymptotics will be employed to improve accuracy and power for these post-selection inference procedures.

许多统计分析使用模型选择程序。也许最常见的模型选择问题是线性回归中的变量选择问题。选择的原则动机包括对可解释性的渴望，预防过度拟合以及对统计能力的关注。当数据具有高维度时，就会产生一种实际动机，并且比观察更大的解释变量。相关的应用涵盖了从神经科学，医学和物理学到经济学，社会学和心理学的整个科学探究领域。现在可以使用大量的可变选择程序目录，统计社区将其重点转移到了选择后的推理问题上。当使用相同的数据选择模型并推断该模型时，统计推断的标准方法不再有效。从根本上重要的是要有精确的选择后推理程序，这些推理程序也足够强大，可以检测到观察到的科学假设的偏离，并避免在有限样本中精确推断所需的强大分布假设。这项研究旨在开发既准确又强大的选择后推理方法，特别是减少取决于样本量的统计错误。该项目的目的是进一步理解选择后推断的渐近理论，尤其是基于Covtest和Covtest和Trunced Gaussian（TG）统计量的选择性推断，以及使用后选择间隔（POSI）程序的同时推断。前两个过程可以通过选择性错误控制，即选定模型参数的错误控制。 POSI方法旨在控制所有可能的子模型参数的家庭错误率。尽管这些程序产生了有效的选择后推断，但如果没有强烈的假设，它们尤其容易受到违反关键假设的影响，而在小型到中等样本大小的现实环境中，例如过度保存或不准确的置信区间和低功率。在这个项目中，将采用渐近膨胀，鞍点近似，引导程序和来自高阶渐近学的相关技术，以提高这些选择后推理程序的准确性和功率。