Abstract
A method for constructing signatures of random reparametrizations of periodic functions is presented.
The proposed signatures are functions, which contain information about the height and order of local extrema of the observation. In contrast to other statistical methods for reparametrized curves, the observations can be of different lengths and the construction does not involve aligning them.
The signature is shown to be stable with respect to changes in the distribution of reparametrizations and to enjoy standard CLT properties, including in the case of dependent observations.
The positioning of a vehicle based on magnetic signals is the industrial application which motivated this work.
Ongoing work with Frédéric Chazal and Bertrand Michel.
References
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