LOCAL LINEAR MODELLING OF THE CONDITIONAL DISTRIBUTION FUNCTION FOR FUNCTIONAL ERGODIC DATA-Reference-Cited by-同舟云学术

LOCAL LINEAR MODELLING OF THE CONDITIONAL DISTRIBUTION FUNCTION FOR FUNCTIONAL ERGODIC DATA

Published:2022-08-12 Issue:3 Volume:27 Page:360-382
ISSN:1392-6292
Container-title:Mathematical Modelling and Analysis
language:
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Author:

Ayad Somia¹,Laksaci Ali²,Rahmani Saâdia¹^ORCID,Rouane Rachida¹

Affiliation:

1. Laboratory of Stochastic Models, Statistics and Applications, University of Saida–Dr. Moulay Tahar, 20000 Saida, Algeria

2. Department of Mathematics, College of Science, King Khalid University, 61413 Abha, Saudi Arabia

Abstract

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.

Publisher

Vilnius Gediminas Technical University

Subject

Modeling and Simulation,Analysis

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