Recursive estimation in a class of models of deformation

TL;DR

This paper introduces a recursive estimation method for shape invariant models with multiple parameters, extending existing work to multivariate cases and demonstrating convergence on simulated and real ECG data.

Contribution

It develops a recursive estimation framework for multivariate shape invariant models, combining Robbins-Monro and Nadaraya-Watson estimators with proven convergence properties.

Findings

Estimates converge almost surely and are asymptotically normal.

Method effectively estimates shape, translation, and scale parameters.

Validated on simulated and real ECG datasets.

Abstract

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 main pattern 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.