Data of Complex Type

Statistics, as any other mathematical science, is changing, and the change is coming from the current data types that are collected and from the need to analyze these data sets, which no longer consist in numbers, but in complex entities, such a medical devices outputs, ribonucleic acid (RNA) sequences, trees, graphs, or digital camera images, to mention just a few. Using computational techniques from such entities, one may extract mathematical elements, nowadays called objects , that can be represented as points on certain metric spaces known as object spaces which have a smooth structure on an open dense subset. In this chapter, we provide just a small number of examples of such complex data to familiarize the reader with them. For more examples, of the smooth type, see e.g., Patrangenaru and Ellingson (2015) [ 106 ], Dryden and Mardia (2016) [ 39 ] or Marron and Dryden (2022) [ 92 ].