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This paper deals with the problem of the nonparametric analysis by the relative-error regression when the explanatory of a variable is of infinite dimension. Based on k-Nearest Neighbors procedure (kNN), we construct an estimator and establish its asymptotic properties. Precisely, we show its Uniform consistency in Number of Neighbors (UNN) with the precision of the convergence rate. Some empirical studies are also performed to highlight the impact of this asymptotic result in nonparametric functional statistics. [ABSTRACT FROM AUTHOR]

This article deals with the equivariant non parametric robust regression estimation for stationary ergodic processes valued in F × R , where F is a semi-metric space. We consider a new robust regression estimator when the scale parameter is unknown. The principal aim is to prove the almost complete convergence (with rate) for the proposed estimator. Unlike in standard multivariate cases, the gap between pointwise and uniform results is not immediate. So, suitable topological considerations are needed, implying changes in the rates of convergence which are quantified by entropy considerations. [ABSTRACT FROM AUTHOR]

L1-norm approach is used to construct the local linear estimator of the spatial regression quantile for functional regressors. Under mixing spatial condition, we establish the almost complete convergence of the constructed approach. The applicability of the constructed estimator is examined by a Monte-Carlo study. The finite sample performance of the proposed estimator is compared to the classical kernel estimator of the functional spatial quantile regression. The result indicates that our new approach is more accurate than the classical one. [ABSTRACT FROM AUTHOR]