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Survey estimators of domain means under shape restrictions

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dc.contributor.authorOliva Avilés, Cristian M., author
dc.contributor.authorMeyer, Mary C., advisor
dc.contributor.authorOpsomer, Jean D., advisor
dc.contributor.authorBreidt, F. Jay, committee member
dc.contributor.authorWang, Haonan, committee member
dc.contributor.authorWilson, Kenneth R., committee member
dc.date.accessioned2018-09-10T20:04:22Z
dc.date.available2018-09-10T20:04:22Z
dc.date.issued2018
dc.description.abstractNovel 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.
dc.format.mediumborn digital
dc.format.mediumdoctoral dissertations
dc.identifierOlivaAviles_colostate_0053A_14886.pdf
dc.identifier.urihttps://hdl.handle.net/10217/191301
dc.languageEnglish
dc.language.isoeng
dc.publisherColorado State University. Libraries
dc.relation.ispartof2000-2019
dc.rightsCopyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright.
dc.subjectestimation
dc.subjectsampling
dc.subjectsurvey
dc.subjectinference
dc.subjectdomain mean
dc.subjectshape-constrained
dc.titleSurvey estimators of domain means under shape restrictions
dc.typeText
dcterms.rights.dplaThis Item is protected by copyright and/or related rights (https://rightsstatements.org/vocab/InC/1.0/). You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
thesis.degree.disciplineStatistics
thesis.degree.grantorColorado State University
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy (Ph.D.)

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