In this paper, we study the equivariant nonparametric robust regression estimation relationship between a functional dependent random covariable and a scalar response. We consider a new robust regression estimator when the scale parameter is unknown. The consistency result of the proposed estimator is studied, namely the uniform almost complete convergence (with rate). Thus, suitable topological considerations are needed, implying changes in the convergence rates, which are quantified by entropy considerations. The benefits of considering robust estimators are illustrated on two real data sets where the robust fit reveals the presence of influential outliers.
Mokhtaria, Mebsout; Kadi, Attouch M.; and Omar, Fetitah
Nonparametric M-regression with Scale Parameter For Functional Dependent Data,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 15,
2, Article 8.
Available at: https://digitalcommons.pvamu.edu/aam/vol15/iss2/8