Shape-Constrained Estimation and Inference for Surveys

Colorado State University, Fort Collins CO

Investigators

Abstract

This research project will provide a new class of tools for survey practitioners to improve the stability and precision of survey estimates. Surveys represent a key source of data for government, business, and academics. The cost of conducting surveys has increased dramatically during the last decade, however, while response rates have declined. The new methods developed by this project will take advantage of "soft" or vague information often available in practice in many different contexts but not directly used or used in only "ad hoc" ways. This information is referred to as "shape constraints" in statistics. The new shape-constrained survey estimation tools will represent an important advance in design-based estimation, which continues to be the primary approach used in large-scale government surveys. At the same time, this work will be the first application of shape constraints in the survey context. The new tools will be especially useful for large-scale survey agencies and have the potential to lead to considerably improved efficiency and to result in estimates that satisfy the qualitative properties expected by data users. The investigators will develop user-friendly software. This research project will develop new survey estimation methods for a variety of different types of shape constraints that can be encountered in practice, together with statistical tools to assess whether the shape constraint holds in the survey population and to estimate the precision of the estimates. Shape-constrained estimation will be introduced in several important survey methodological areas of practical interest, including in estimation for sub-populations, post-stratification, adjusting for nonresponse and small area estimation. The research will result in new statistical algorithms for weighted constrained estimation, in statistical testing methods for the validity of the shape constraints for survey data, and in a new class of weight calibration methods that are based on shape constraints. The project is supported by the Methodology, Measurement, and Statistics Program and a consortium of federal statistical agencies as part of a joint activity to support research on survey and statistical methodology.