# Backward nested descriptors asymptotics with inference on stem cell differentiation

@article{Huckemann2016BackwardND, title={Backward nested descriptors asymptotics with inference on stem cell differentiation}, author={Stephan F. Huckemann and Benjamin Eltzner}, journal={The Annals of Statistics}, year={2016} }

For sequences of random backward nested subspaces as occur, say, in dimension reduction for manifold or stratified space valued data, asymptotic results are derived. In fact, we formulate our results more generally for backward nested families of descriptors (BNFD). 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 BNFD can be…

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