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Abstract:
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In various application fields such as internet traffic monitoring, medical imagery, or signal processing, modern technology has allowed for the routine collection of data from populations with a high temporal and/or spatial resolution. Such data sets appear as collections of curves or functions and are thus commonly termed functional data. In this presentation we look into the nonparametric estimation of the trend in a functional data set. We elaborate general consistency results and convergence rates as the numbers of sampled curves and design points go to infinity. We also derive asymptotic normality results in spaces of functions and apply them to simultaneous confidence bands procedures. These bands procedures, which may be used for data exploration as well as for inference tasks (e.g. testing the goodness-of-fit of parametric models), are finally compared in a numerical study.
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