Author ORCID Identifier

http://orcid.org/0000-0001-7821-6993

Year of Publication

2016

Degree Name

Doctor of Philosophy (PhD)

Document Type

Doctoral Dissertation

College

Arts and Sciences

Department

Statistics

First Advisor

Dr. Richard J. Kryscio

Second Advisor

Dr. Li Chen

Abstract

In this dissertation, we develop unified and efficient nonparametric statistical methods for estimating and comparing environmental exposure distributions in presence of detection limits. In the first part, we propose a kernel-smoothed nonparametric estimator for the exposure distribution without imposing any independence assumption between the exposure level and detection limit. We show that the proposed estimator is consistent and asymptotically normal. Simulation studies demonstrate that the proposed estimator performs well in practical situations. A colon cancer study is provided for illustration. In the second part, we develop a class of test statistics to compare exposure distributions between two groups by using the integrated weighted difference in the kernel-smoothed estimator proposed in the first part. We study the conditions on the weight function such that the test statistics are stable, i.e. the asymptotic variances are finite. Simulation studies demonstrate that the proposed tests preserve type I errors regardless whether the distributions of the detection limit in the two groups differ or not and are more efficient than current methods in certain situations. A colon cancer study is provided for illustration. In the third part, we extend the estimation and testing methods developed in the part one and two to survey data by incorporating sampling weights. The results of several simulation studies are reported to demonstrate the performance of the proposed methods. The Jackknife method is utilized for the variance estimation to account for complex sample designs.

Digital Object Identifier (DOI)

https://doi.org/10.13023/ETD.2016.467

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