Computer Intensive Methods in Sampling and in Adaptive Contexts

点击翻译按钮获取中文摘要

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.