On the nonparametric estimation of the functional expectile regression

Mohammedi, Mustapha; Bouzebda, Salim; Laksaci, Ali

doi:10.5802/crmath.27

Cited by 6 publications

(1 citation statement)

References 15 publications

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“…Indeed, classical regression provides us with a high sensitivity to extreme values, allowing for more reactive risk management. Quantile regression, on the other hand, provides the ability to acquire exhaustive information on the effect of the explanatory variable on the response variable by examining its conditional distribution; refer to [77][78][79] for further details on expectiles in functional data settings.…”

Section: The Conditional Quantilementioning

confidence: 99%

Wavelet Density and Regression Estimators for Continuous Time Functional Stationary and Ergodic Processes

Didi

Bouzebda

2022

Mathematics

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In this study, we look at the wavelet basis for nonparametric estimation of density and regression functions for continuous functional stationary processes in Hilbert space. The mean integrated squared error for a small subset is established. We employ a martingale approach to obtain the asymptotic properties of these wavelet estimators. These findings are established under rather broad assumptions. All we assume about the data is that it is ergodic, but beyond that, we make no assumptions. In this paper, the mean integrated squared error findings in the independence or mixing setting were generalized to the ergodic setting. The theoretical results presented in this study are (or will be) valuable resources for various cutting-edge functional data analysis applications. Applications include conditional distribution, conditional quantile, entropy, and curve discrimination.

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Section: The Conditional Quantilementioning

confidence: 99%