92796 - Advanced Topics In Statistics For (Fuzzy) Set-Valued Data

Learning outcomes

By the end of the course the student learns the advanced methods and the operational tools for the analysis of (fuzzy) set-valued data. The student is able to face the theoretical problems of analyzing these kind of data and its generalizations and to use statistical software for estimating the statistical models in an effective and coherent way.

Course contents

• Introduction: ``Non-precise'' data

  • Examples of interval data

  • Generalizations of interval data

    • Dimension: (compact and convex) set-valued data

    • Smooth' characteristic function: fuzzy set-valued data

  • R-package starshapesets

• Interval data: structures and statistics

  • Arithmetic and metric

  • Statistical measures

  • Inference

• Structures and statistics for the extensions

  • Compact and convex sets

  • Star-shaped sets

  • Fuzzy sets

• Regression

  • Linear models

  • The model MG: constrained least-squares

  • Inference

Readings/Bibliography

• W. Trutschnig, G. Gonzalez-Rodriguez, A. Colubi, M.A. Gil, A new family of metrics for compact, convex (fuzzy) sets based on a generalized concept of mid and spread, Information Sciences, 179, 2009, 3964-3972.

• G. Gonzalez-Rodriguez, A. B. Ramos-Guajardo, A. Colubi, A. Blanco-Fernandez, A new framework for the statistical analysis of set-valued random elements, International Journal of Approximate Reasoning 92, 2018, Pages 279-294

• A. Colubi, G. Gonzalez-Rodriguez, Fuzziness in data analysis: Towards accuracy and robustness, Fuzzy Sets and Systems 281, 2015, Pages 260-271

• A. Blanco-Fernandez, et al. A distance-based statistical analysis of fuzzy number-valued data, International Journal of Approximate Reasoning 55, Issue

• M.B. Ferraro, R. Coppi, G. Gonzalez Rodriguez, A. Colubi, A linear regression model for imprecise response, International Journal of Approximate Reasoning,

• A. Blanco-Fernandez, A. Colubi, M. Garcia-Barzana, A set arithmetic-based linear regression model for modelling interval-valued responses through real-valued variables, Information Sciences 247, 2013

• A. Colubi, G. Gonzalez-Rodriguez, M.A. Gil, Wolfgang Trutschnig, Nonparametric criteria for supervised classification of fuzzy data, International Journal of Approximate Reasoning 52, Issue 9, 2011

• A.B. Ramos-Guajardo, A. Colubi, G. Gonzalez-Rodriguez, Inclusion degree tests for the Aumann expectation of a random interval, Information Sciences 288, 2014, Pages 412-422

Teaching methods

Problem-based learning

Assessment methods

Students will be evaluated on a pass/fail basis.

The successful completion of the course will be evaluated through the presentation of case studies during the lessons. Students who cannot participate during the course will be examined orally on flexible individually agreed dates.

Teaching tools

Software: R

Office hours

See the website of Ana Maria Colubi Cervero