Estimation of the distribution of random shifts deformation

Ismael Castillo (1) , Jean-Michel Loubes (2)

1 faculty of exact sciences, section stochastics
2 IMT - Institut de Mathématiques de Toulouse UMR5219

Consider discrete values of functions shifted by unobserved translation effects, which are independent realizations of a random variable with unknown distribution $\mu$, modeling the variability in the response of each individual. Our aim is to construct a nonparametric estimator of the density of these random translation deformations using semiparametric preliminary estimates of the shifts. Building on results of Dalalyan et al. (2006), semiparametric estimators are obtained in our discrete framework and their performance studied. From these estimates we construct a nonparametric estimator of the target density. Both rates of convergence and an algorithm to construct the estimator are provided.

Mots clés: Semiparametric statistics; Order two properties; Penalized Maximum Likelihood; Practical algorithms.; Practical algorithms

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Ismael Castillo, Jean-Michel Loubes. Estimation of the distribution of random shifts deformation. 2008. ⟨hal-00347826⟩