Non parametric estimation of the structural expectation of a stochastic increasing function

TL;DR

This paper proposes a nonparametric warping model for functional data to estimate a mean pattern called the structural expectation, accounting for small variations among curves, with proven consistency and asymptotic normality of the estimators.

Contribution

It introduces a novel nonparametric approach to estimate the structural expectation of stochastic increasing functions, including empirical estimators and their theoretical properties.

Findings

Empirical estimators are consistent.

Estimators exhibit asymptotic normality.

Method effectively captures main behavior of functional data.

Abstract

This article introduces a non parametric warping model for functional data. When the outcome of an experiment is a sample of curves, data can be seen as realizations of a stochastic process, which takes into account the small variations between the different observed curves. The aim of this work is to define a mean pattern which represents the main behaviour of the set of all the realizations. So we define the structural expectation of the underlying stochastic function. Then we provide empirical estimators of this structural expectation and of each individual warping function. Consistency and asymptotic normality for such estimators are proved.