Distances and inference for covariance functions
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).Full text not available from this repository.
Official URL: http://www2.warwick.ac.uk/fac/sci/statistics/crism...
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
|Item Type:||Working or Discussion Paper (Working Paper)|
|Divisions:||Faculty of Science > Statistics|
|Series Name:||CRiSM reports|
|Publisher:||University of Warwick, Dept. of Statistics|
|Place of Publication:||Coventry|
|Number of Pages:||20|
|Status:||Not Peer Reviewed|
|Access rights to Published version:||Open Access|
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