Extrinsic Data Analysis on Sample Spaces with a Manifold Stratification

Given a random object on a stratified space embedded in a numerical space, often times the extrinsic sample means stick to a stratum that is closest to the population mean of the corresponding probability distribution in the ambient numerical space via this embedding. In the case of an open book, the limiting distribution of the extrinsic sample means supported on this possibly lower dimensional stratum, is extrinsically Gaussian on that stratum. Applications of the classical single stratum case to various types image data analysis, including to medical imaging, are also given.