Symbolic data analysis: statistical inference on interval-valued data regression

Interval-valued data are one of the most common forms of symbolic data. Previous studies have provided a number of approaches to conduct linear regression models for interval data, while few have involved issues surrounding inference on the regression coefficient estimates. In this dissertation, we propose a method of statistical inference on coefficient estimates for interval data regression by means of the maximum likelihood principle. Under some assumptions, this method not only enables us to provide point estimators of the parameters in linear regression models, but also gives the distributions of the point estimators, as well as the confidence intervals. Performances of the proposed method are evaluated by simulationsas well as real data analyses.