Internship Project
Business and Economics

Regression for density-valued data

Institution
Humboldt-Universität zu Berlin
Chair of Statistics, School of Business and Economics
Subject Area
Statistics
Availability
Summer Term Internship 2023:
08 May – 28 July
 22 May – 11 August
 05 June – 25 August
 
Individual Timeframe Internship:
The dates are arranged individually according to the project's and the student's availability.
 
Internship Modality:
On-site internship in Berlin
Project Supervisor(s)
Prof. Dr. Sonja Greven
Academic Level
Advanced undergraduate students (from third year) 
Master's students 
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. We have recently developed a regression framework to relate densities to other variables of interest such as age, gender or location (Maier et al., 2021); see https://arxiv.org/abs/2110.11771.
In this project, we will further develop regression models that take densities as covariates and/or outcomes. Envisioned extensions concern the extension to bivariate densities (e.g. both incomes for men and women in a couple), the extension to densities measured with an error or varying precision, and/or extensions to interaction terms if a scalar outcome refers to an individual that is also part of the covariate density/composition. 
The project would ideally be jointly addressed by a PhD student and a Bachelor student (close to finishing).
Tasks for Interns
  • Developing the model
  • Developing and implement an estimation approach
  • Simulation study
  • Application to actual data, e.g. to the STAR data on peer effects in education or to income data from a collaborative project in gender economics
  • Writing of a scientific report.
Academic Level
Advanced undergraduate students (from third year) 
Master's students 
Ph.D. students 
Requirements
  • Prior knowledge on compositional data analysis and preferably the Bayes space methodology as well as functional data analysis
  • Prior knowledge on regression
  • Good general background in Statistics
  • Experience with computations in the statistical software R and with data applications
Expected Preparation
Literature research on regression for compositional data, functional data, density data
Familiarization with at least one suitable data set as application 
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For more information on the Humboldt Internship Program or the project, please contact the program coordinator.