Internship Project
Business and Economics

Multivariate compositional splines

Institution
Humboldt-Universität zu Berlin
Chair of Statistics, School of Business and Economics
Subject Area
Statistics
Availability
Position 2023 filled


Internship Modality:
On-site internship in Berlin
Project Supervisor(s)
Prof. Dr. Sonja Greven
Academic Level
Ph.D. students 
Language
English
Further Information
Project Type
Academic Research
Project Content
Densities occur as data objects in many areas, reflecting, for example, income distributions, distributions of particle sizes in sediments, or class compositions in schools. Multivariate densities are highly relevant to looking at association structures in data and methods for their analysis, thus of high importance.
This project will develop the theoretical framework for two-dimensional and multivariate compositional splines based on one-dimensional compositional splines. This will include their construction and application in smoothing (multivariate) probability density functions embedded in the Bayes space methodology. Results will be significant in their own right and a building block for density models.
Tasks for Interns
  • Development of the construction of two-dimensional compositional splines using tensor products.
  • Construction of two-dimensional compositional smoothing splines. 
  • Generalization to the multivariate case.
  • Application on bivariate and multivariate data sets.

Academic Level
Ph.D. students 
Requirements
  • Master's degree in Applied Mathematics or similar.
  • Interest in numerical mathematics and statistics.
  • Knowledge of software R, Matlab.

Expected Preparation
Reading on compositional splines, tensor product bases, Bayes spaces, and statistical methods for densities.

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For more information on the Humboldt Internship Program or the project, please contact the program coordinator.