Local linear modelling of the conditional distribution function for functional ergodic data
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.
Keyword : ergodic sata, functional data, local linear estimator, conditional distribution function, nonparametric estimation, asymptotic properties
This work is licensed under a Creative Commons Attribution 4.0 International License.
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