Resampling Methods for Survey Data with Extensions in other Contexts

给定的统计数据有多准确？这可能是研究人员在使用统计数据来估计感兴趣的参数时提出的第一个问题。通过分析方法获得给定统计量（如方差）的精确度量并不总是容易的。这就是为什么重采样方法，如自举法，在文献中被广泛使用来估计这些测量。在我的研究计划中，我打算研究bootstrap方法的理论发展和实际应用，以建立新的想法。******加拿大统计局为研究人员提供了访问包含自举权重列的数据文件的途径。这些权重解释了观测值中的抽样可变性，可以很容易地用于计算估计量的方差或构造置信区间。不幸的是，生活很少那么简单，统计调查中的一个重要实际问题是大多数数据文件中存在项目无响应。项目无响应通常使用填充数据文件中的空单元格的输入来补偿。将输入值视为观测值可能会导致对点估计量方差的严重低估，因为用于全响应调查数据的自举方法既没有考虑项目无响应的可变性，也没有考虑输入。我计划在假设响应概率不相等和调查设计复杂的情况下，为输入的调查数据建立自举方法。******自举法广泛应用于不同的统计领域。应用估计方程的广义自举法估计模型参数估计的方差。在这种方法下，我们打算在金融和流行病学应用的自相关计数数据时间序列的半参数回归模型中找到最优自举权重。******在另一个应用程序中，我打算为流行的队列生存数据开发一个bootstrap方法。这种数据的一种特殊情况是长度偏右截尾数据。兴趣主要来自于一些加拿大统计学家在分析作为加拿大健康与老龄化调查研究的一部分收集的痴呆症患者生存数据时面临的挑战。现有的这种生存数据的自举方法没有考虑左截断分布中额外的可用信息。因此，这种自举方法效率不高。我计划针对这类数据开发一种高效的bootstrap方法。研究这种情况下的叠刀重采样方法也是我研究的一部分。在插入式估计器由于正确的审查和/或有偏差的抽样而经常产生偏差的情况下，折刀方法通常旨在减少偏差。******这些项目将改进目前的统计技术并产生新的实用方法，同时培训将在加拿大学术界或工业界工作的强大统计学家。

How accurate is a given statistic? This might be the first question that a researcher asks once a statistic is used to estimate a parameter of interest. Obtaining accuracy measures of a given statistic, such as the variance, is not always easy through analytical methods. That is why resampling methods, such as the bootstrap, have been widely used in the literature to estimate such measurements. In my research program, I intend to study the theoretical developments and practical applications of bootstrap methods in order to establish new ideas.******Statistics Canada provides researchers with access to data files containing columns of bootstrap weights. These weights account for sampling variability in the observations and can be easily used to compute the variance of estimators or construct confidence intervals. Unfortunately, life is rarely that simple and one important practical problem in statistical surveys is the presence of item non-response in most data files. Item non-response is usually compensated using imputation which fills the empty cells in the data file. Treating the imputed values as if they were observed values may lead to serious underestimation of the variance of point estimators since bootstrap methods for full response survey data take into account neither the variability due to item non-response, nor imputation. I plan to build bootstrap methods for imputed survey data assuming the cases of unequal response probabilities and complex survey designs. ******The bootstrap is widely applied in different statistical areas. The generalized bootstrap for estimating equations is applied to estimate the variance of model parameter estimates. Under this approach, we intend to find optimal bootstrap weights in the case of a semi-parametric regression model for autocorrelated time series of count data with applications in finance and epidemiology.******In another application, I intend to develop a bootstrap method for prevalent cohort survival data. A special case of such data is length-biased right censored data. Interest mostly stems from challenges that some Canadian statisticians were faced with while analyzing survival with dementia data collected as part of the Canadian Study of Health and Aging survey. The existing bootstrap methods for such survival data do not consider the extra available information in the left truncation distribution. Thus, such bootstrap methodologies are not efficient. I plan to develop an efficient bootstrap method tailored for such data. Studying jackknife resampling methods in such settings is also a part of my research. The jackknife methods are usually aim at reducing bias where the plug-in estimators are often biased due to right censoring and/or biased sampling. ******These projects will improve current statistical techniques and produce new practical approaches while training strong statisticians who will work in academia or industry in Canada.