Statistical inference for functional data based on a generalization of Mahalanobis distance
Tuesday 14th October 2014
Ghiglietti, A.; Paganoni, A.M.
In this paper we propose a generalization of Mahalanobis distance that extends the usual multivariate one to functional data generated by stochastic processes. We show that this distance is well defined in L2 and achieves both the goals of (i) considering all the infinite components of data basis expansion and (ii) keeping the same ideas on which is based the Mahalanobis distance. This new mathematical tool is adopted in an inferential context to construct tests on the mean of Gaussian processes for one and two populations. The tests are constructed assuming the covariance structure to be either know or unknown. The power of all the critical regions has been computed analytically. A wide discussion on the behavior of these tests in terms of their power functions is realized, supported by some simulation studies.