Pigoli, Davide, Aston, John A. D., Dryden, I. L. and Secchi, Piercesare (2012) Distances and inference for covariance functions. Working Paper. Coventry: University of Warwick, Dept. of Statistics. CRiSM reports, Vol.2012 (No.12-14).

Research output not available from this repository.

Request-a-Copy directly from author or use local Library Get it For Me service.

Request Changes to record.

Abstract

A framework is developed for inference concerning the covariance operator of a functional random
process, where the covariance operator itself is an object of interest for the statistical analysis. Distances
for comparing positive definite covariance matrices are either extended or shown to be inapplicable for
functional data. In particular, an infinite dimensional analogue of the Procrustes size and shape distance is
developed. The convergence of the finite dimensional approximations to the infinite dimensional distance
metrics is also shown. To perform inference, a Frechet estimator for the average covariance function is ´
introduced, and a permutation procedure to test the equality of the covariance operator between two groups
is then considered.
The proposed techniques are applied to two problems where inference concerning the covariance is
of interest. Firstly, in data arising from a study into cerebral aneurysms, it is of interest to determine
whether two groups of data can be combined when comparing with a third group. For this to be done,
it is necessary to assess whether the covariance structures of the two groups are the same or different.
Secondly, in a philological study of cross-linguistic dependence, the use of covariance operators has been
suggested as a way to incorporate quantitative phonetic information. It is shown that distances between
languages derived from phonetic covariance functions can provide insight into relationships between the
Romance languages.

Item Type:	Working or Discussion Paper (Working Paper)
Divisions:	Faculty of Science, Engineering and Medicine > Science > Statistics
Series Name:	CRiSM reports
Publisher:	University of Warwick, Dept. of Statistics
Place of Publication:	Coventry
Official Date:	2012
Dates:	Date Event 2012 Published
Volume:	Vol.2012
Number:	No.12-14
Number of Pages:	20
Status:	Not Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Open Access (Creative Commons)

Request changes or add full text files to a record

Repository staff actions (login required)

View Item