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Compositional regression with functional response
- Source :
- Computational Statistics & Data Analysis. 123:66-85
- Publication Year :
- 2018
- Publisher :
- Elsevier BV, 2018.
-
Abstract
- The problem of performing functional linear regression when the response variable is represented as a probability density function (PDF) is addressed. PDFs are interpreted as functional compositions, which are objects carrying primarily relative information. In this context, the unit integral constraint allows to single out one of the possible representations of a class of equivalent measures. On these bases, a function-on-scalar regression model with distributional response is proposed, by relying on the theory of Bayes Hilbert spaces. The geometry of Bayes spaces allows capturing all the key inherent features of distributional data (e.g., scale invariance, relative scale). A B-spline basis expansion combined with a functional version of the centered log-ratio transformation is utilized for actual computations. For this purpose, a new key result is proved to characterize B-spline representations in Bayes spaces. The potential of the methodological developments is shown on simulated data and a real case study, dealing with metabolomics data. A bootstrap-based study is performed for the uncertainty quantification of the obtained estimates.
- Subjects :
- Statistics and Probability
Computer science
Probability density function
010502 geochemistry & geophysics
01 natural sciences
Bayes spaces, Regression analysis, Density functions, B-spline representation
010104 statistics & probability
symbols.namesake
Bayes' theorem
0101 mathematics
Uncertainty quantification
0105 earth and related environmental sciences
Variable (mathematics)
Applied Mathematics
Hilbert space
Regression analysis
B-spline representation
Bayes spaces
Constraint (information theory)
Computational Mathematics
Transformation (function)
Computational Theory and Mathematics
symbols
Density functions
Algorithm
Subjects
Details
- ISSN :
- 01679473
- Volume :
- 123
- Database :
- OpenAIRE
- Journal :
- Computational Statistics & Data Analysis
- Accession number :
- edsair.doi.dedup.....6049d0a0438f21d438e4c8af139284bf