Aboubacar Amiri

Recursive estimation of nonparametric regression with functional covariate

The main purpose is to estimate the regression function of a real random variable with functional explanatory variable by using a recursive nonparametric kernel approach. The mean square error and the almost sure convergence of a family of recursive kernel estimates of the regression function are derived. These results are established with rates and precise evaluation of the constant terms. Also, a central limit theorem for this class of estimators is established. The method is evaluated on simulations and real dataset studies.

Recursive regression estimators with application to nonparametric prediction

In the case of dependent data, the purpose of this paper is to establish the exact asymptotic quadratic error of a parametric family of recursive kernel regression estimators. Based on this family of estimators, recursive nonparametric kernel predictors are studied. For mixing Markov processes, their almost sure convergence to the best predictor is established. Efficiency of these methods is also shown through numerical simulations highlighting their significantly reduced time of computation.

Consistency of the recursive nonparametric regression estimation for dependent functional data

We consider the recursive estimation of a regression functional where the explanatory variables take values in some functional space. We prove the almost sure convergence of such estimates for dependent functional data. Also we derive the mean quadratic error of the considered class of estimators. Our results are established with rates and asymptotic appear bounds, under strong mixing condition. Finally, the feasibility of the proposed estimator is illustrated throughout an empirical study.