Date of Award

6-2016

Degree Name

Doctor of Philosophy

Department

Statistics

First Advisor

Dr. Magdalena Niewiadomska-Bugaj

Second Advisor

Dr. Steven Kohler

Third Advisor

Dr. Rajib Paul

Fourth Advisor

Dr. Je rey Terpstra

Keywords

Nondetects, simulations, bootstrap, lognormal, gamma, statistical methodology

Abstract

Limitations of instruments used to collect continuous data sometimes lead to obtaining observations lower than a limit of detection. These observations are known as nondetects. They could be zeroes, or positive numbers, but they are too small to be recorded by a measuring device. Nondetects frequently occur in environmental data. Trace amounts of chemicals can exist in soil or groundwater and are undetectable by a machine reading. These observations pose a problem to researchers since the true values are unknown.

Simulations in the literature have led to inconsistent conclusions regarding what estimation technique to use with nondetect data when estimating the population mean. Researchers have used di ering distributional assumptions, sample sizes, number of detection limits, and proportions of nondetects when conducting simulations. Many researchers base conclusions on distributional assumptions which are not valid in all environmental datasets. Furthermore, the majority of research involves data with one detection limit and data that is not a mixture of multiple distributions.

The simulations in this research comprehensively investigate lognormal and gamma data with two detection limits as well as non-unimodal lognormal and gamma mixtures. Mean estimation techniques are used to create bootstrap intervals for the population mean. Guidance is given to researchers who wish to estimate a population mean using a dataset from an unknown distribution with multiple detection limits.

Access Setting

Dissertation-Open Access

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