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，以提供关于各种重要主题的可靠当前统计数据。使用有效的抽样设计来最小化指定精度的成本。使用可变性度量(标准误差和可信区间)来评估样本统计的质量。调查的目的通常是为具有足够大样本的亚总体提供可靠的估计。另一方面，对可靠的当地(或小范围)统计数据的需求日益增长，这些统计数据是制定政策和方案、分配资金和营销决策所需的。当地地区的样本量可能很小，甚至为零，传统的直接估计无法提供所需精度的当地估计。有必要求助于基于模型的方法，这种方法可以通过基于人口普查和行政记录等辅助数据的链接模型，跨相关领域借用信息。加拿大统计局在其现代化举措中纳入了基于模型的小区域估计。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，也可以得到可靠的估计。我2003年的Wiley书[1]和它的第二版[2]关于小区域估计已经成为研究人员和用户的标准参考。我建议继续我在小区域估计方面的工作，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健康科学家和其他人广泛用于研究关系和检验感兴趣的假设，例如来自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会导致错误的推断。为了解决这一问题，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，其中包含作出有效推断所需的足够信息。我建议开发统一的方法，仅使用结合数据文件中提供的调查权重的标准软件，就公共使用数据文件中感兴趣的参数提供有效的假设和可信区间测试。由于回复率下降，与传统抽样调查相关的成本增加，以及其他数据来源的可获得性，如社交媒体数据、网络调查和行政记录，近年来，将来自多个来源的数据结合起来进行推断的专题受到了极大的关注。加拿大统计局在其官方统计举措现代化过程中优先考虑这一主题。我建议通过开发合适的方法来研究这一重要课题，这些方法可以减少与非概率样本和概率样本相结合的选择偏差，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.