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Essays in Empirical Bayes Methods.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Essays in Empirical Bayes Methods./
Author:	Ho, Sheng Chao.
Description:	1 online resource (147 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 85-12, Section: B.
Contained By:	Dissertations Abstracts International85-12B.
Subject:	Statistics. -
Online resource:	click for full text (PQDT)
ISBN:	9798382830032

Essays in Empirical Bayes Methods.
Ho, Sheng Chao.

Essays in Empirical Bayes Methods. - 1 online resource (147 pages)

Source: Dissertations Abstracts International, Volume: 85-12, Section: B.

Thesis (Ph.D.)--University of Pennsylvania, 2024.

Includes bibliographical references

This dissertation develops empirical Bayes methods for large-scale estimation. Researchers are now interested in leveraging increasingly large datasets for estimation of heterogeneous parameters, in fields ranging from teacher value-added estimation to developing optimal large-scale forecasts, where the number of parameters is typically in the thousands. The problem of estimating teacher value-added serves as the running example throughout the dissertation, and as such also forms the basis of both chapters' empirical applications.The first chapter develops shrinkage estimation that is robust to unobserved sorting between multiple dimensions of fixed effects. We motivate an estimator class through a hierarchical Bayes perspective that is shown to nest the common shrinkage estimators, such as the one-way fixed effects estimator prominent in the teacher value-added literature. We provide an algorithm of optimizing within this class that results in a feasible estimator that is asymptotically optimal within the entire class. We then consider extending the estimator class in empirically relevant directions, such as in modeling sorting directly through the prior that further sharpens estimation.The second chapter addresses the problem of optimal estimation under unknown heteroskedasticity, where we consider a generalization of the objective from the usual unit-specific means to now unit-specific quantiles. The unknown heteroskedasticity renders the common shrinkage estimators infeasible, because the optimal amount of shrinkage depends precisely on the unknown sampling variance. We provide an extension of the Tweedie's formula and show that the compound optimal mean and quantile estimators depend only on density of certain sufficient statistics. We then exploit this to propose feasible, asymptotic compound optimal estimators.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2024

Mode of access: World Wide Web

ISBN: 9798382830032Subjects--Topical Terms:

556824
Statistics.
Subjects--Index Terms:

Bayes methodsIndex Terms--Genre/Form:

554714
Electronic books.

Essays in Empirical Bayes Methods.
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504 $a Includes bibliographical references
520 $a This dissertation develops empirical Bayes methods for large-scale estimation. Researchers are now interested in leveraging increasingly large datasets for estimation of heterogeneous parameters, in fields ranging from teacher value-added estimation to developing optimal large-scale forecasts, where the number of parameters is typically in the thousands. The problem of estimating teacher value-added serves as the running example throughout the dissertation, and as such also forms the basis of both chapters' empirical applications.The first chapter develops shrinkage estimation that is robust to unobserved sorting between multiple dimensions of fixed effects. We motivate an estimator class through a hierarchical Bayes perspective that is shown to nest the common shrinkage estimators, such as the one-way fixed effects estimator prominent in the teacher value-added literature. We provide an algorithm of optimizing within this class that results in a feasible estimator that is asymptotically optimal within the entire class. We then consider extending the estimator class in empirically relevant directions, such as in modeling sorting directly through the prior that further sharpens estimation.The second chapter addresses the problem of optimal estimation under unknown heteroskedasticity, where we consider a generalization of the objective from the usual unit-specific means to now unit-specific quantiles. The unknown heteroskedasticity renders the common shrinkage estimators infeasible, because the optimal amount of shrinkage depends precisely on the unknown sampling variance. We provide an extension of the Tweedie's formula and show that the compound optimal mean and quantile estimators depend only on density of certain sufficient statistics. We then exploit this to propose feasible, asymptotic compound optimal estimators.
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