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Functional data analysis: local linear estimation of the \(L_1\)-conditional quantiles. (English) Zbl 1427.62146

Summary: We consider a new estimator of the quantile function of a scalar response variable given a functional random variable. This new estimator is based on the \(L_1\) approach. Under standard assumptions, we prove the almost-complete consistency as well as the asymptotic normality of this estimator. This new approach is also illustrated through some simulated data and its superiority, compared to the classical method, has been proved for practical purposes.

MSC:

62R10 Functional data analysis
62G08 Nonparametric regression and quantile regression
62G20 Asymptotic properties of nonparametric inference
62G35 Nonparametric robustness
62G07 Density estimation
62H12 Estimation in multivariate analysis

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