Stephan Huckemann (Georg-August University Göttingen)

Backward Nested Descriptors Asymptotics with Inference on Stem Cell Differentiation

joint work with Benjamin Eltzner

Abstract: For sequences of random backward nested subspaces as occur, say, in dimension reduction
for manifold or stratified space valued data, asymptotic results are derived. Under rather general
conditions, asymptotic strong consistency holds. Under additional, still rather general hypotheses, among
them existence of a.s. local twice differentiable charts, asymptotic joint normality of a BNDF can be
shown. If charts factor suitably, this leads to individual asymptotic normality for the last element,
a principal nested mean or a principal nested geodesic, say. It turns out that these results pertain to
principal nested spheres (PNS) analysis by Jung et al. 2010. We derive a nested bootstrap two-sample test,
and apply PNS to track early human mesenchymal stem cell differentiation over a coarse time grid
to locate a change point with direct consequences for the design of further studies.