Survey estimators of domain means under shape restrictions
Date
2018
Authors
Oliva Avilés, Cristian M., author
Meyer, Mary C., advisor
Opsomer, Jean D., advisor
Breidt, F. Jay, committee member
Wang, Haonan, committee member
Wilson, Kenneth R., committee member
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Abstract
Novel methodologies that introduce shape-restricted regression techniques into survey domain estimation and inference are presented in this dissertation. Although population domain means are frequently expected to respect shape constraints that arise naturally on the survey data, their most common direct estimators often violate such restrictions, especially when the variability of these estimators is high. Recently, a monotone estimator that is obtained from adaptively pooling neighboring domains was proposed. When the monotonicity assumption on population domain means is reasonable, the monotone estimator leads to asymptotically valid estimation and inference, and can lead to substantial improvements in efficiency, in comparison with unconstrained estimators. Motivated from these convenient properties adherent to the monotone estimator, the two main questions addressed in this dissertation arise: first, since invalid monotone restrictions may lead to biased estimators, how to create a data-driven decision for whether a restriction violation on the sample occurs due to an actual violation on the population, or simply because of chance; and secondly, how the monotone estimator can be extended to a more general constrained estimator that allows for many other types of shape restrictions beyond monotonicity. In this dissertation, the Cone Information Criterion for Survey Data (CICs) is proposed to detect monotonicity departures on population domain means. The CICs is shown to lead to a consistent methodology that makes an asymptotically correct decision when choosing between unconstrained and constrained domain mean estimators. In addition, a design-based estimator of domain means that respect inequality constraints represented through irreducible matrices is presented. This constrained estimator is shown to be consistent and asymptotically normally distributed under mild conditions, given that the assumed restrictions are reasonable for the population. Further, simulation experiments demonstrate that both estimation and variability of domain means are improved by constrained estimates, in comparison with unconstrained estimates, mainly on domains with small sample sizes. These proposed methodologies are applied to analyze data from the 2011-2012 U.S. National Health and Nutrition Examination Survey and the 2015 U.S. National Survey of College Graduates. In terms of software development and outside of the survey context, the package bcgam is developed in R to fit constrained generalised additive models using a Bayesian approach. The main routines of bcgam allow users to easily specify their model of interest, and to produce numerical and graphical output. The package bcgam is now available from the Comprehensive R Archive Network.
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Subject
estimation
sampling
survey
inference
domain mean
shape-constrained