Given k independent samples of functional data the problem of testing the null hypothesis of equality of their respective mean functions is considered. So the setting is quite similar to that of the classical one-way anova model but the k samples under study consist of functional data. A simple natural test for this problem is proposed. It can be seen as an… (More)
The bootstrap methodology for functional data and functional estimation target is considered. A Monte Carlo study analyzing the performance of the bootstrap confidence bands (obtained with different resampling methods) of several functional estimators is presented. Some of these estimators (e.g., the trimmed functional mean) rely on the use of depth notions… (More)
In this paper we extend the notion of impartial trimming to a functional data framework, and we obtain resistant estimates of the center of a functional distribution. We give mild conditions for the existence and uniqueness of the functional trimmed means. We show the continuity of the population parameter with respect to the weak convergence of probability… (More)
The possibility of considering random projections to identify probability distributions belonging to parametric families is explored. The results are based on considerations involving invariance properties of the family of distributions as well as on the random way of choosing the projections. In particular, it is shown that if a one-dimensional (suitably)… (More)
Abreviated Title: Qualitative Robustness SUMMARY In this paper we generalize Hampel's definition of robustness and IT-robustness of a sequence of estimators to the case of non i.i.d. stochastic processes, using appropriate metrics on the space of finite and infinite dimensional samples. We also present a different approach to qualitative robust-ness based… (More)
We propose a new robust estimation method based on random projections that is adaptive and, automatically produces a robust estimate, while enabling easy computations for high or infinite dimensional data. Under some restricted contamination models, the procedure is robust and attains full efficiency. We tested the method using both simulated and real data.