Computer Intensive Methods in Sampling and in Adaptive Contexts

采样和自适应环境中的计算机密集型方法

• 批准号: RGPIN-2016-05686
• 负责人: Léger, Christian
• 金额: $ 2.19万
• 依托单位: Université de Montréal
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=759375
• 关键词: Computer; Intensive; Methods; Sampling; Adaptive

Fast computing has allowed statisticians to develop new statistical methods that would have been unthinkable before due to the impossibility to use them in practice. One example is the bootstrap. It can be used to compute variance estimates for complicated estimators or construct confidence intervals. The main goal of this research program is to improve the theoretical and practical understanding of these methods to develop sound new statistical procedures.Companies and governments require the best possible information to make the best decisions. Statistics Canada collects important data which are available to researchers who can extract its information for the benefit of society. Unfortunately, some units in the sample do not respond to some of the questions leading to item non-response. To overcome the bias that can result, imputation of these missing observations based on a model is used. Also, using methodology developed in Canada in Rao, Wu & Yue (1992), the data files contain bootstrap weights that allow researchers to assess the variability of estimators such as the population total or median. But these bootstrap weights only reflect the variability from the selection of the sample units, ignoring the extra variability due to imputation.In the last grant, we studied bootstrap methods that can correctly estimate the variance of imputed estimators of a population total. We will study how these methods perform when studying other parameters, such as the median. In particular, we will show that the bootstrap weights approach works for such parameters using the differential properties of statistical functionals.In statistics, a certain methodology is often adapted to a different area. Non-response in survey sampling is similar to dropping-out in longitudinal studies where patients are followed during a certain period and some patients leave the study for whatever reason. We will study bootstrap methods that would be doubly robust in their assessment of the variability of a doubly robust estimator, i.e., an estimator that will work provided that either the data model or the drop-out model is correct.Another common situation for researchers is to estimate the linear relationship between one variable and a number of explanatory variables where not all of them are needed. In that case, a variable selection method is used to choose which ones are really necessary. An important practical problem is to construct a confidence interval for all variables, including those which are left out, that will take into account the model selection step. We are studying the use of bootstrap methods for this problem.These projects will advance statistical methodology. But at least as importantly, they will provide exciting challenges to train the next generation of highly qualified statisticians to teach and do research in universities, as well as work in industry wherever information needs to be extracted from data.

快速计算使统计学家能够开发新的统计方法，这在以前是不可想象的，因为无法在实践中使用它们。一个例子是引导程序。 它可用于计算复杂估计量的方差估计或构建置信区间。该研究计划的主要目标是提高对这些方法的理论和实践理解，以开发合理的新统计程序。公司和政府需要尽可能最佳的信息来做出最佳决策。 加拿大统计局收集重要数据，研究人员可以利用这些数据提取信息，造福社会。不幸的是，样本中的某些单位没有回答导致项目不回答的一些问题。为了克服可能产生的偏差，使用基于模型的对这些缺失观测值的插补。此外，使用加拿大 Rao、Wu 和 Yue (1992) 开发的方法，数据文件包含引导权重，使研究人员能够评估估计量的变异性，例如总体总数或中位数。但这些引导权重仅反映了样本单位选择的变异性，忽略了由于插补而产生的额外变异性。在上一次资助中，我们研究了可以正确估计总体总数的插补估计量方差的引导方法。我们将在研究其他参数（例如中位数）时研究这些方法的表现。特别是，我们将使用统计泛函的微分属性来证明引导权重方法适用于此类参数。在统计学中，某种方法通常适用于不同的领域。调查抽样中的无答复类似于纵向研究中的退出，其中患者在一定时期内被跟踪，并且一些患者因任何原因退出研究。我们将研究在评估双鲁棒估计量的变异性时具有双鲁棒性的引导方法，即只要数据模型或退出模型正确，该估计量就可以工作。研究人员的另一种常见情况是估计一个变量与多个解释变量之间的线性关系，但不需要所有解释变量。 在这种情况下，使用变量选择方法来选择哪些是真正必要的。一个重要的实际问题是为所有变量（包括那些被遗漏的变量）构建一个置信区间，该区间将考虑模型选择步骤。我们正在研究使用引导方法来解决这个问题。这些项目将推进统计方法。但至少同样重要的是，它们将提供令人兴奋的挑战，以培训下一代高素质统计学家在大学教学和研究，以及在需要从数据中提取信息的行业工作。