A Robbins-Monro procedure for a class of models of deformation

Philippe Fraysse (1)

1 ALEA - Advanced Learning Evolutionary Algorithms

The paper deals with the statistical analysis of several data sets as- sociated with shape invariant models with different translation, height and scaling parameters. We propose to estimate these parameters together with the common shape function. Our approach extends the recent work of Bercu and Fraysse to multivariate shape invariant models. We propose a very efficient Robbins-Monro procedure for the estimation of the translation parameters and we use these esti- mates in order to evaluate scale parameters. The main pattern is estimated by a weighted Nadaraya-Watson estimator. We provide almost sure convergence and asymptotic normality for all estimators. Finally, we illustrate the convergence of our estimation procedure on simulated data as well as on real ECG data.

Mots clés: Semiparametric estimation; estimation of shifts; estimation of a regression function; asymptotic properties

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

Philippe Fraysse. A Robbins-Monro procedure for a class of models of deformation. 2012. ⟨hal-00696050⟩