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Title: Customizing the dimensionality of functional data Authors:  Enea Bongiorno - Universita del Piemonte Orientale (Italy)
Aldo Goia - Universita' del Piemonte Orientale (Italy) [presenting]
Abstract: The representation of functional data in a small dimension is a very important task. Usually, it is performed by using the well-known truncated Karhunen-Loeve expansion where the truncation threshold is selected suitably: it is a global method since once the dimension is chosen it is used for all the curves. Nevertheless, this approach is not optimal in the sense that some curves could be represented in a lower dimension and for other ones a larger dimension would be desirable. To obtain a more parsimonious representation of the data, a local dimensionality reduction method can be used: it is based on a nonparametric estimate of the correction term appearing in a Small ball probability factorization for functional Hilbert data. The latter can be interpreted as a measure of the quality of the representation of functional data in small dimensions and its theoretical properties are investigated. To assess the ability of the local selection approach, some applications to simulated and real datasets are performed.