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With large-scale database systems, statistical analysis of data, formed byprobability distributions, become an important task in explorative dataanalysis. Nevertheless, due to specific properties of density functions, theirproper statistical treatment still represents a challenging task in functionaldata analysis. Namely, the usual L2 metric does not fully accounts for therelative character of information, carried by density functions; instead, theirgeometrical features are followed by Bayes spaces of measures. The easiestpossibility of expressing density functions in L2 space is to use centredlogratio transformation, nevertheless, it results in functional data with aconstant integral constraint that needs to be taken into account for furtheranalysis. While theoretical background for reasonable analysis of densityfunctions is already provided comprehensively by Bayes spaces themselves,preprocessing issues still need to be developed. The aim of this paper is tointroduce optimal smoothing splines for centred logratio transformed densityfunctions that take all their specific features into account and provide aconcise methodology for reasonable preprocessing of raw (discretized)distributional observations. Theoretical developments are illustrated with areal-world data set from official statistics.

Preprocessing of centred logratio transformed density functions using smoothing splines