ABSTRACT
Chapters 4 through 6 provided general theory for adapting inferential metho-
dology for multivariate data to the analysis of data lying on finite-dimensional
manifolds. However, for data arising on infinite-dimensional Hilbert mani-
folds, methodology for inference must be adapted instead from techniques de-
veloped for data analysis on Hilbert spaces, as described in Chapter 2. As far
as infinite dimensional data analysis is concerned, in this chapter our scope is
limited to considering only the extension of the neighborhood hypothesis me-
thodology on Hilbert spaces in Section 2.15, to the case of Hilbert manifolds.
Applications of this material to shape analysis of planar contours can be found
in Chapter 18. The primary reference for this chapter is Ellingson et al. (2013)
[104].
