Local linear modelling of the conditional distribution function for functional ergodic data

    Somia Ayad Affiliation
    ; Ali Laksaci Affiliation
    ; Saâdia Rahmani   Affiliation
    ; Rachida Rouane Affiliation


The focus of functional data analysis has been mostly on independent functional observations. It is therefore hoped that the present contribution will provide an informative account of a useful approach that merges the ideas of the ergodic theory and the functional data analysis by using the local linear approach. More precisely, we aim, in this paper, to estimate the conditional distribution function (CDF) of a scalar response variable given a random variable taking values in a semimetric space. Under the ergodicity assumption, we study the uniform almost complete convergence (with a rate), as well as the asymptotic normality of the constructed estimator. The relevance of the proposed estimator is verified through a simulation study.

Keyword : ergodic sata, functional data, local linear estimator, conditional distribution function, nonparametric estimation, asymptotic properties

How to Cite
Ayad, S., Laksaci, A., Rahmani, S., & Rouane, R. (2022). Local linear modelling of the conditional distribution function for functional ergodic data. Mathematical Modelling and Analysis, 27(3), 360–382.
Published in Issue
Aug 12, 2022
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This work is licensed under a Creative Commons Attribution 4.0 International License.


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