Semiparametric estimation of plane similarities: application to fast computation of aeronautic loads

ABSTRACT

In the big data era, it is often needed to resolve the problem of parsimonious data representation. In this paper, the data under study are curves and the sparse representation is based on a semiparametric model. Indeed, we propose an original registration model for noisy curves. The model is built transforming an unknown function by plane similarities. We develop a statistical method that allows to estimate the parameters characterizing the plane similarities. The properties of the statistical procedure are studied. We show the convergence and the asymptotic normality of the estimators. Numerical simulations and a real-life aeronautic example illustrate and demonstrate the strength of our methodology.

KEYWORDS:

• Semiparametric model
• registration of curves
• statistical learning of a physical system

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 62F12
• 62F30
• 62P30

Acknowledgements

We are very much indebted to the referees and the Associate Editor for their constructive criticisms, comments and remarks that resulted in a major improvement of the original manuscript. We would also like to thank Fabrice Gamboa and Christian Bes for careful re-readings and thoughtful advice.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Edouard Fournier  http://orcid.org/0000-0002-4133-5267