New models for symbolic data analysis

Abstract Symbolic data analysis (SDA) is an emerging area of statistics concerned with understanding and modelling that takes distributional form (i.e. symbols ), such as random lists, intervals histograms. It was developed under the premise statistical unit interest symbol, inference required at this level. Here we consider a different perspective, which opens new research direction in field SDA. We assume that, standard analysis, level individual-level data. However, are unobserved, aggregated into observed symbols—group-based distributional-valued summaries—prior to analysis. introduce novel general method for constructing likelihood functions symbolic based on desired probability model underlying measurement-level data, while only observing summaries. This approach door classes symbol design construction, addition developing SDA viable tool enable improve upon classical analyses, particularly very large complex datasets. illustrate through several real simulated including study multivariate construction techniques.