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Title: Nonparametric regression for locally stationary functional data Authors:  Aboubacar Amiri - Charles de Gaulle University (France) [presenting]
Abstract: The problem of the nonparametric regression of a real random variable on a non-stationary time series of functional data is addressed. We focus on the estimation of the regression function using a kernel approach. We introduce an estimator of the regression operator that takes into account the non-stationary behavior of the data-generating process. The mean square error and the almost sure convergence of the proposed estimator are derived. In addition, a central limit theorem on the regression estimator is established. Asymptotic results are established with convergence rates, whereas the asymptotic constants are explicitly calculated by assuming that the covariate is a local stationary and strong mixing functional process.