Date of Award:

8-2023

Document Type:

Thesis

Degree Name:

Master of Science (MS)

Department:

Mathematics and Statistics

Committee Chair(s)

Yan Sun

Committee

Yan Sun

Committee

Brennan Bean

Committee

D. Richard Cutler

Abstract

There is a growing demand for the development of new statistical models and the refinement of established methods to accommodate different data structures. This need arises from the recognition that traditional statistics often assume the value of each observation to be precise, which may not hold true in many real-world scenarios. Factors such as the collection process and technological advancements can introduce imprecision and uncertainty into the data.

For example, consider data collected over a long period of time, where newer measurement tools may offer greater accuracy and provide more information than previous methods. In such cases, it becomes crucial to restructure the data to account for imprecision and incorporate uncertainty into the analysis.

Furthermore, the increasing availability of large datasets has introduced computational challenges in analyzing and processing the data. Representing the data in terms of intervals can help address this uncertainty by reducing the data size or accommodating imprecision. Traditional methods have already embraced this concept, but given the rising popularity of machine learning, it is essential to develop models for interval-valued data within the machine learning framework.

Tree-based methods, in particular, are well-suited for handling interval-valued data due to their robustness to outliers and their nonparametric nature. Therefore, we propose a new model that takes into account the natural structure of the interval-valued data.. These tree-based methods offer improvements over existing models for interval-valued data, providing a framework capable of effectively handling data with uncertainty arising from imprecision or the need for size management.

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