Recursive estimation in a class of models of deformation

The paper deals with the statistical analysis of several data sets associated 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 estimates in order to evaluate scale parameters. The common shape function is estimated by a weighted Nadaraya–Watson recursive 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.