Name
Abstract | ||
|---|---|---|
Probability density functions are frequently used to characterize the distributional properties of large-scale database systems. As functional compositions, densities primarily carry relative information. As such, standard methods of functional data analysis (FDA) are not appropriate for their statistical processing. The specific features of density functions are accounted for in Bayes spaces, which result from the generalization to the infinite dimensional setting of the Aitchison geometry for compositional data. The aim is to build up a concise methodology for functional principal component analysis of densities. A simplicial functional principal component analysis (SFPCA) is proposed, based on the geometry of the Bayes space B 2 of functional compositions. SFPCA is performed by exploiting the centred log-ratio transform, an isometric isomorphism between B 2 and L 2 which enables one to resort to standard FDA tools. The advantages of the proposed approach with respect to existing techniques are demonstrated using simulated data and a real-world example of population pyramids in Upper Austria. |
Year | DOI | Venue |
|---|---|---|
2016 | 10.1016/j.csda.2015.07.007 | Computational Statistics & Data Analysis |
Keywords | Field | DocType |
Compositional data,Bayes spaces,Centred log-ratio transformation,Functional principal component analysis | Econometrics,Functional principal component analysis,Functional data analysis,Compositional data,Isomorphism,Statistics,Probability density function,Principal component analysis,Mathematics,Statistical processing,Bayes' theorem | Journal |
Volume | Issue | ISSN |
94 | C | 0167-9473 |
Citations | PageRank | References |
5 | 0.58 | 6 |
Authors | ||
5 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Karel Hron | 1 | 13 | 5.01 |
| Alessandra Menafoglio | 2 | 17 | 5.25 |
| matthias templ | 3 | 78 | 9.50 |
| Klara Hruzová | 4 | 5 | 0.58 |
| Peter Filzmoser | 5 | 5 | 0.58 |