On the Identifiability of the Functional Convolution Model, Giles Hooker, 9-9-13

On the Identifiability of the Functional Convolution Model

Giles Hooker(Submitted on 9 Sep 2013)

This report details conditions under which the Functional Convolution Model described in \citet{AHG13} can be identified from Ordinary Least Squares estimates without either dimension reduction or smoothing penalties. We demonstrate that if the covariate functions are not spanned by the space of solutions to linear differential equations, the functional coefficients in the model are uniquely determined in the Sobolev space of functions with absolutely continuous second derivatives.

Subjects: Statistics Theory (math.ST)Cite as: arXiv:1309.2178 [math.ST]  (or arXiv:1309.2178v1 [math.ST] for this version)