Asymptotic normality of random fields of positively or negatively associated processes
Journal of Multivariate Analysis
Nonparametric Functional Data Analysis: Theory and Practice (Springer Series in Statistics)
Nonparametric Functional Data Analysis: Theory and Practice (Springer Series in Statistics)
Local smoothing regression with functional data
Computational Statistics
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We consider the estimation of the regression operator r in the functional model: Y=r(x)+@e, where the explanatory variable x is of functional fixed-design type, the response Y is a real random variable and the error process @e is a second order stationary process. We construct the kernel type estimate of r from functional data curves and correlated errors. Then we study their performances in terms of the mean square convergence and the convergence in probability. In particular, we consider the cases of short and long range error processes. When the errors are negatively correlated or come from a short memory process, the asymptotic normality of this estimate is derived. Finally, some simulation studies are conducted for a fractional autoregressive integrated moving average and for an Ornstein-Uhlenbeck error processes.