Date of Award:

5-2024

Document Type:

Thesis

Degree Name:

Master of Science (MS)

Department:

Mathematics and Statistics

Committee Chair(s)

Yan Sun

Committee

Yan Sun

Committee

Daniel Coster

Committee

John Stevens

Abstract

In recent years, interval data has become an increasingly popular tool to solve modern data problems. Intervals are now often used for dimensionality reduction, data aggregation, privacy censorship, and quantifying awareness of various uncertainties. Among many statistical methods that are being studied and developed for interval data, the significance test is particularly of importance due to its fundamental value both in theory and practice. The difficulty in developing such tests mainly lies in the fact that the concept of normality does not extend naturally to interval data (due the range of an interval being necessarily non-negative), causing the exact tests to be hard to formulate. In the literature, tests for comparing means of one or two sample interval data have been developed, which motivates the exploration of the multi-sample case. In this thesis, we propose a novel asymptotic (as the sample size goes to infinity) method for comparing multi-sample means with interval data. This procedure builds a test statistic based on a ratio of between-group interval variance and within-group interval variance. The theoretical results for this procedure are derived. Simulation results with both discrete and continuous data validate our procedure, and show promising small sample performances. Finally, we apply our method to ground snow load interval data, where we are able to detect interval mean differences across regions in Canada.

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