Small area estimation, combining data from multiple sources, and inference from non-probability samples

基于概率抽样的抽样调查被加拿大统计局和其他机构广泛使用，以提供关于各种重要主题的可靠的当前统计数据。有效的采样设计用于在给定精度下最小化成本。可变性测量（标准误差和置信区间）用于评估样本统计的质量。调查通常旨在为样本足够大的亚种群提供可靠的估计。另一方面，对可靠的地方（或小区域）统计数据的需求日益增长，这些数据在制定政策和计划、资金分配和营销决策中都是必需的。局部区域内的样本量可能非常小甚至为零，传统的直接估计无法提供理想精度的局部估计。有必要求助于基于模型的方法，这些方法可以通过基于辅助数据（如人口普查和行政记录）的链接模型来跨相关领域借用信息。加拿大统计局已将基于模型的小面积估算纳入其现代化举措。我对基于模型的小区域估计进行了广泛的研究，即使在小区域内的样本量很小的情况下，也可以得出可靠的估计。我2003年Wiley出版的关于小面积估算的书[1]及其第二版[2]已经成为研究人员和用户的标准参考。我建议继续我在小面积估计方面的工作，并提供健壮的方法来解决实际问题，如模型错误规范。抽样调查数据被社会和卫生科学家及其他人广泛用于研究关系和检验感兴趣的假设，例如加拿大全国公共卫生调查的纵向数据。忽略设计复杂性的标准方法可能导致错误的推断。为了解决这个问题，加拿大统计局和其他一些机构提供了公共使用的数据文件，其中载有作出有效推论所需的充分资料。我建议开发统一的方法，仅使用包含数据文件中提供的调查权重的标准软件，对公共使用数据文件中感兴趣的参数的假设和置信区间进行有效检验。由于与传统抽样调查相关的回复率下降和成本增加，以及其他数据来源（如社交媒体数据、网络调查和行政记录）的可用性，近年来，将多个来源的数据结合起来进行推断的话题受到了很多关注。加拿大统计局在其官方统计倡议的现代化中优先考虑了这一问题。我建议通过开发合适的方法来开展这一重要主题的研究，这些方法可以减少与非概率样本结合概率样本相关的选择偏差，并导致有效的估计。

Sample surveys, based on probability sampling, are widely used by Statistics Canada and other agencies to provide reliable current statistics on a variety of important topics. Efficient sampling designs are used to minimize the cost for a specified precision. Measures of variability (standard errors and confidence intervals) are used to assess the quality of the sample statistics. Surveys are typically designed to provide reliable estimates for sub-populations with sufficiently large samples. On the other hand, there is a growing demand for reliable local (or small area) statistics that are needed in formulating policies and programs, allocation of funds and marketing decisions. Sample sizes within local areas can be very small or even zero and the traditional direct estimates cannot provide local estimates with desired precision. It becomes necessary to resort to model-based methods that can borrow information across related domains through linking models based on auxiliary data such as censuses and administrative records. Statistics Canada has included model-based small area estimation in their modernization initiatives. I have done extensive research on model-based small area estimation that can lead to reliable estimates even when the sample sizes are small within small areas. My 2003 Wiley book [1] and its second edition [2] on small area estimation have become standard references to researchers and users. I propose to continue my work on small area estimation and provide robust methods to address practical issues such as model mis-specifications. Sample survey data are extensively used by social and health scientists and others to study relationships and testing hypotheses of interest, e.g. longitudinal data from the National Public Health Survey of Canada. Standard methods that ignore the design complexities can lead to erroneous inferences. To address this problem, Statistics Canada and some other agencies provide public-use data files containing adequate information for making valid inferences. I propose to develop unified methods that can provide valid tests of hypotheses and confidence intervals on parameters of interest from the public-use data files, using only standard software that incorporates survey weights supplied in the data files. Due to decreasing response rates and increasing costs associated with traditional sample surveys and availability of other sources of data, such as social media data, web surveys and administrative records, the topic of combining data from multiple sources to make inferences has received a lot of attention in recent years. Statistics Canada has given priority to this topic in their modernization of official statistics initiatives. I propose to conduct research on this important topic by developing suitable methods that can reduce selection bias associated with non-probability samples combined with probability samples and lead to efficient estimates.