Mathematics Ph.D. Dissertations

Statistical Inferences On Inflated Data Based On Modified Empirical Likelihood

Date of Award

2020

Document Type

Dissertation

Degree Name

Doctor of Philosophy (Ph.D.)

Department

Statistics

First Advisor

Wei Ning (Advisor)

Second Advisor

Chen Hanfeng (Committee Member)

Third Advisor

Junfeng Shang (Committee Member)

Fourth Advisor

Rachel Shafer (Other)

Abstract

Many studies deal with inflated and nonnegative data, such as in medical studies. Most studies that deal with inflated data deal with zero-inflated datasets, but there are many datasets that are zero-one inflated as well. Zero-inflated datasets are characterized by a significant proportion of zero values, leading to a skewed distribution. Zero-One inflated datasets are characterized by a significant proportion of zero and one values, which also leads to a skewed distribution.

It is common practice to use the Central Limit Theorem to assume an approximately normal distribution to construct confidence intervals and conduct hypothesis tests. However with inflated and highly skewed distributions, this practice leads to an inaccurate result. The empirical likelihood method offers an alternative method of computing confidence intervals with the benefit of having no distributional assumptions. Although the empirical likelihood method provides an improvement, it suffers from several drawbacks.

In this dissertation, we propose several modified empirical likelihood methods to combat these drawbacks. We use these modified methods, along with the empirical likelihood and normal approximation methods, to construct confidence intervals based on zero-inflated data and zero-one inflated data. We compare the performance of each method for these two situations on both simulated data and real data. Furthermore, we develop a hypothesis test for comparing two means based on one of the modified empirical likelihood approaches. We then test the modified empirical likelihood approach against the empirical likelihood and normal approximation methods using simulated and real data.

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