Computer Intensive Methods in Sampling and in Adaptive Contexts

快速计算使统计学家能够开发新的统计方法，这些方法在以前是不可想象的，因为不可能在实践中使用它们。一个例子是bootstrap。 它可用于计算复杂估计量的方差估计或构造置信区间。该研究项目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。公司和政府需要最好的信息来做出最好的决策。 加拿大统计局收集重要数据，研究人员可以从中提取信息，造福社会。不幸的是，样本中的一些单位没有回答一些问题，导致项目没有回答。为了克服可能导致的偏倚，使用基于模型的这些缺失观察值的插补。此外，使用Rao，Wu & Yue（1992）在加拿大开发的方法，数据文件包含自举权重，允许研究人员评估估计量的可变性，如人口总数或中位数。但是这些Bootstrap权重只反映了样本单位选择的变异性，而忽略了由于插补引起的额外变异性。在上一个研究项目中，我们研究了Bootstrap方法，它可以正确估计总体总量的插补估计量的方差。我们将研究这些方法在研究其他参数（如中位数）时的表现。特别地，我们将使用统计泛函的微分性质来证明自举权重方法适用于这些参数。在统计学中，某种方法通常适用于不同的领域。调查抽样中的无应答类似于纵向研究中的脱落，在纵向研究中，患者在一定时期内接受随访，一些患者因任何原因离开研究。我们将研究bootstrap方法，该方法在评估双重稳健估计的变异性时具有双重稳健性，即，一种估计量，只要数据模型或退出模型是正确的，它就能工作。研究人员的另一种常见情况是估计一个变量和许多解释变量之间的线性关系，而不是所有这些变量都需要。 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构建置信区间，包括那些被遗漏的变量，这将考虑到模型选择步骤。我们正在研究如何使用自助法来解决这个问题，这些项目将促进统计方法的发展。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的统计学家，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。

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.