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

加拿大统计局和其他机构广泛使用以概率抽样为基础的抽样调查，就各种重要专题提供可靠的最新统计数据。有效的抽样设计用于最小化指定精度的成本。变异性的量度（标准误差和置信区间）用于评估样本统计的质量。调查的目的通常是为样本足够大的次群体提供可靠的估计数。另一方面，对可靠的地方（或小地区）统计数据的需求日益增加，这是制定政策和方案、分配资金和营销决策所必需的。局部区域内的样本量可能很小甚至为零，传统的直接估计无法提供具有期望精度的局部估计。有必要采用基于模型的方法，通过将基于人口普查和行政记录等辅助数据的模型联系起来，借用相关领域的信息。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，即使在小区域内样本量很小的情况下，也可以进行可靠的估计。我在2003年出版的Wiley著作[1]及其第二版[2]中关于小面积估算的内容已经成为研究人员和用户的标准参考。我建议继续我的工作，小面积估计，并提供强大的方法来解决实际问题，如模型误规格。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，例如加拿大国家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。为解决这一问题，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断所需的充分信息。我建议开发统一的方法，可以提供有效的测试的假设和置信区间的参数感兴趣的公共使用的数据文件，只使用标准的软件，结合调查的权重提供的数据文件。由于传统抽样调查的答复率不断下降，成本不断增加，以及社交媒体数据、网络调查和行政记录等其他数据来源的可用性，近年来，将多个来源的数据结合起来进行推断的问题受到了广泛关注。加拿大统计局在官方统计现代化倡议中优先重视这一专题。我建议通过开发合适的方法，可以减少与非概率样本结合概率样本的选择偏差，并导致有效的估计，对这一重要课题进行研究。

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.