Degree Type

Dissertation

Date of Award

2009

Degree Name

Doctor of Philosophy

Department

Statistics

First Advisor

Jean D. Opsomer

Abstract

Variance estimation for survey estimators that include modeling relies on approximations that ignore the effect of fitting the models. Cross-validation (CV) criterion provides a way to incorporate this effect. We will show 4 ways in which we explore this in this dissertation.

Penalized spline regression, as a main type of nonparametric model assisted methods, is a common technique to improve the precision of finite population estimators. In Chapter 1, we propose a CV based criterion to select the smoothing parameter for the penalized spline regression estimator. The design-based asymptotic properties of the method are derived, and simulation studies show how well it works in practice.

Regression estimator is a common technique to improve the precision of finite population estimators by using the available auxiliary information of the population. In Chapter 2, we propose a CV based variance estimator and compare it to other two variance estimators. The design-based asymptotic properties of the estimator are derived, and simulation studies show how well it works in practice.

Regression estimator works well for the cases where there is a strong linear relationship between regressor and regressands. On the contrary, when the relationship is weak, π estimator is a good choice. In Chapter 3, a new estimator as a linear combination of those two estimators is proposed to select between them. We introduce a CV based variance estimator for the new proposed estimator. The design-based asymptotic properties of the estimator

are explored, and simulation studies show how well it works in practice.

In linear regression estimation, how to choose the set of control variables x is a difficult practical problem. In Chapter 4, a CV criterion is introduced for choosing between combinations of the x variables to be included in the model. The design-based asymptotic properties of the estimator are explored, and simulation studies show how well it works in practice.

DOI

https://doi.org/10.31274/etd-180810-1609

Copyright Owner

Lifeng You

Language

en

Date Available

2012-04-28

File Format

application/pdf

File Size

148 pages

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