Density modelling with functional data analysis

Recent technological advances have eased the collection of big amounts of data in many research fields. In this scenario density estimation may represent an important source of information. One dimensional density functions represent a special case of functional data subject to the constraints to be non negative and with a constant integral equal to one. Because of these constraints, a naive application of functional data analysis (FDA) methods may lead to non-valid results. To solve this problem, by means of an appropriate transformation densities are embedded in the Hilbert space of square integrable functions where standard FDA methodologies can be applied.