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

点击翻译按钮获取中文摘要

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.