Title: New models for symbolic data analysis,
Abstract: Symbolic data analysis (SDA) is an emerging area of statistics based on
aggregating individual level data into group-based distributional summaries
(symbols), and then developing statistical methods to analyse them. It is ideal
for analysing large and complex datasets, and has immense potential to become a
standard inferential technique in the near future. However, existing SDA
techniques are either non-inferential, do not easily permit meaningful
statistical models, are unable to distinguish between competing models, and are
based on simplifying assumptions that are known to be false. Further, the
procedure for constructing symbols from the underlying data is erroneously not
considered relevant to the resulting statistical analysis. In this paper we
introduce a new general method for constructing likelihood functions for
symbolic data based on a desired probability model for the underlying classical
data, while only observing the distributional summaries. This approach resolves
many of the conceptual and practical issues with current SDA methods, opens the
door for new classes of symbol design and construction, in addition to
developing SDA as a viable tool to enable and improve upon classical data
analyses, particularly for very large and complex datasets. This work creates a
new direction for SDA research, which we illustrate through several real and
simulated data analyses.