A Symmetrical Model Applied to Interval-Valued Data Containing Outliers with Heavy-Tail Distribution

Abstract

The aim of Symbolic Data Analysis (SDA) is to provide a set of techniques to summarize large data sets into smaller ones called symbolic data tables. This paper considers a kind of symbolic data called Interval-Valued Data (IVD) which stores data intrinsic variability and/or uncertainty from the original data set. Recent works have been proposed to fit the classic linear regression model to symbolic data. However, those works do not consider the presence of symbolic data outliers. Generally, most specialists treat outliers as errors and discard them. Nevertheless, a single interval-data outlier holds significant information which should not be discarded or ignored. This work introduces a prediction method for IVD based on the symmetrical linear regression (SLR) analysis whose response model is less susceptible to the IVD outliers. The model considers a symmetrical distribution for error which allows to the model possibility of applying regular statistical hypothesis tests.