We present some asymptotic results on the distance between the means of samples of curves generated by independent continuous time stochastic processes in L2(T). The asymptotic results are based on mild assumptions on the moments of the processes, and there are no conditions on their probability distribution. The metrics we consider extends the Mahalanobis distance to L2(T) without any truncation on the first principal components. Applications in the context of classification of functional data are finally discussed.
A generalized Mahalanobis distance for the classification of functional data
Andrea Ghiglietti
;
2017-01-01
Abstract
We present some asymptotic results on the distance between the means of samples of curves generated by independent continuous time stochastic processes in L2(T). The asymptotic results are based on mild assumptions on the moments of the processes, and there are no conditions on their probability distribution. The metrics we consider extends the Mahalanobis distance to L2(T) without any truncation on the first principal components. Applications in the context of classification of functional data are finally discussed.
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