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

Edouard Fournier (1) , Stéphane Grihon (2) , Thierry Klein (3)

1 ENAC - Ecole Nationale de l'Aviation Civile
2 Airbus [France]
3 IMT - Institut de Mathématiques de Toulouse UMR5219

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.

Mots clés: Statistical learning of a physical system MSC Classification: 62F12; 62F30; Semiparametric model; 62P30; Registration of curves; Industrial monitoring MSC Classification: 62F12; Statistical learn- ing of a physical system MSC Classification: 62F12

Domaines: Applications [stat.AP]; Autres [stat.ML]

Edouard Fournier, Stéphane Grihon, Thierry Klein. Semiparametric estimation of plane similarities: application to fast computation of aeronautic loads. Statistics, 2019, 53 (5), pp.1168-1186. ⟨10.1080/02331888.2019.1632859⟩. ⟨hal-01879135v3⟩