# Preprocessing of centred logratio transformed density functions using smoothing splines

@article{Machalov2015PreprocessingOC, title={Preprocessing of centred logratio transformed density functions using smoothing splines}, author={Jitka Machalov{\'a} and Karel Hron and Gianna Serafina Monti}, journal={Journal of Applied Statistics}, year={2015}, volume={43}, pages={1419 - 1435} }

With large-scale database systems, statistical analysis of data, occurring in the form of probability distributions, becomes an important task in explorative data analysis. Nevertheless, due to specific properties of density functions, their proper statistical treatment of these data still represents a challenging task in functional data analysis. Namely, the usual metric does not fully accounts for the relative character of information, carried by density functions; instead, their geometrical…

## 23 Citations

Compositional splines for representation of density functions

- Computer ScienceComput. Stat.
- 2021

A new class of spline functions, called compositional splines, are built which can approximate probability density functions in a consistent way and statistical processing of densities using the new approximation tool is demonstrated in case of simplicial functional principal component analysis with anthropometric data.

Simplicial principal component analysis for density functions in Bayes spaces

- MathematicsComput. Stat. Data Anal.
- 2016

Simplicial splines for representation of density functions

- Computer Science
- 2019

A new class of spline functions, called simplicial splines, are built, which can approximate probability density functions in a consistent way, using the Bayes space methodology of density functions.

Changing reference measure in Bayes spaces with applications to functional data analysis

- Mathematics
- 2019

Probability density functions (PDFs) can be understood as continuous compositions by the theory of Bayes spaces. The origin of a Bayes space is determined by a given reference measure. This can be…

Weighting the domain of probability densities in functional data analysis

- MathematicsStat
- 2020

In functional data analysis, some regions of the domain of the functions can be of more interest than others owing to the quality of measurement, relative scale of the domain, or simply some external…

Nonparametric Forecasting of Multivariate Probability Density Functions

- Computer Science, Mathematics
- 2018

A novel nonparametric framework for modelling a time series of copula probability density functions is proposed, which allows to forecast the entire function without the need of post-processing procedures to grant positiveness and unit integral.

Logratio Approach to Distributional Modeling

- MathematicsAdvances in Contemporary Statistics and Econometrics
- 2021

A unifying framework for the discrete and the continuous case based on the theory of Bayes spaces is presented, and it turns out that the centered logratio transformation is a convenient tool for practical computations.

Bivariate Densities in Bayes Spaces: Orthogonal Decomposition and Spline Representation

- Mathematics
- 2020

A new orthogonal decomposition for bivariate probability densities embedded in Bayes Hilbert spaces is derived. It allows one to represent a density into independent and interactive parts, the former…

M E ] 1 9 M ar 2 01 8 Nonparametric forecasting of multivariate probability density functions

- Computer Science
- 2018

A novel nonparametric framework for modelling a time series of copula probability density functions, which allows to forecast the entire function without the need of post-processing procedures to grant positiveness and unit integral is proposed.

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