A1024
Title: IANOVA: Multi-sample means comparisons for imprecise interval data
Authors: Zac Rios - Utah State University (United States)
Yan Sun - Utah State University (United States) [presenting]
Brennan Bean - Utah State University (United States)
Abstract: Interval data has become an increasingly popular tool for solving modern data problems. Intervals are now often used for dimension reduction, data aggregation, privacy censorship, and quantifying awareness of various uncertainties. Among many statistical methods being developed for interval data, the significance test is of particular importance due to its fundamental value both in theory and practice. The difficulty in developing such tests lies mainly in the fact that the concept of normality does not extend naturally to intervals, making the exact tests hard to formulate. As a result, most existing works have relied on bootstrap methods to approximate null distributions. This is not always feasible, considering limited sample sizes or other intrinsic data characteristics in practice. A novel test is proposed for comparing multi-sample means with interval data as a generalization to the classical ANOVA. Based on the random sets theory, the test statistic is constructed analogously to the F statistic for the classical ANOVA. The limiting null distribution is derived under usual assumptions and mild regularity conditions. Simulation studies with various data configurations validate the asymptotic results. Finally, a real interval data ANOVA analysis is presented that showcases the applicability of this new method.
