No abstract

No abstract

The main focus of this work is on providing a formal definition of statistical depth for functional data on the basis of six properties, recognising topological features such as continuity, smoothness and contiguity. Amongst our depth defining properties is one that addresses the delicate challenge of inherent partial observability of functional data, with fulfillment giving rise to a minimal guarantee on the performance of the empirical depth beyond the idealised and practically infeasible case of full observability. As an incidental product, functional depths satisfying our definition achieve a robustness that is commonly ascribed to depth, despite the absence of a formal guarantee in the multivariate definition of depth. We demonstrate the fulfillment or otherwise of our properties for six widely used functional depth proposals, thereby providing a systematic basis for selection of a depth function

No abstract

Functional data analysis and artificial neural networks are the building blocks of the proposed methodology that distinguishes the movement patterns among c’s patients on different stages of the disease and classifies new patients to their appropriate stage of the disease. The movement patterns are obtained by the accelerometer device of android smartphones that the patients carry while moving freely. The proposed methodology is relevant in that it is flexible on the type of data to which it is applied. To exemplify that, it is analyzed a novel real three-dimensional functional dataset where each datum is observed in a different time domain. Not only is it observed on a difference frequency but also the domain of each datum has different length. The obtained classification success rate of 83% indicates the potential of the proposed methodology.