Lab

Applied Statistics And Modelling ASAM

About the lab

Featured projects (4)

Project
Investigating the influence of modeling the fuzziness in data.
Project
We explore the effect decomposition of a principal relationship between binary random variables and propose a valid and useful approach for the analysis of the components of total effect in nonlinear models.
Project
Evaluer la qualité scientifique et la pertinence d'un rapport statistique anonyme sur la question d'un potentiel tourisme électoral à Moutier lors du vote d'appartenance cantonale du 18 juin 2017.

Featured research (4)

We propose a practical procedure of construction of fuzzy confidence intervals by the likelihood method where the observations and the hypotheses are considered to be fuzzy. We use the bootstrap technique to estimate the distribution of the likelihood ratio. The chosen bootstrap algorithm consists on randomly drawing observations by preserving the location and dispersion measures of the original fuzzy data set. A metric $$d_{SGD}^{\theta ^{\star }}$$ d SGD θ ⋆ based on the well-known signed distance measure is considered in this case. We expose a simulation study to investigate the influence of the fuzziness of the computed maximum likelihood estimator on the constructed confidence intervals. Based on these intervals, we introduce a hypothesis test for the equality of means of two groups with its corresponding decision rule. The highlight of this paper is the application of the defended approach on the Swiss SILC Surveys. We empirically investigate the influence of the fuzziness vs. the randomness of the data as well as of the maximum likelihood estimator on the confidence intervals. In addition, we perform an empirical analysis where we compare the mean of the group “Swiss nationality” to the group “Other nationalities” for the variables Satisfaction of health situation and Satisfaction of financial situation.
We develop a fuzzy hypothesis testing approach where we consider the fuzziness of data and the fuzziness of the hypotheses as well. We give the corresponding fuzzy p-value with its \(\alpha \)-cuts. In addition, we use the so-called “signed distance” operator to defuzzify this p-value and we provide the convenient decision rule. Getting a defuzzified p-value and being able to interpret it can be of good use in many situations. We illustrate our testing procedure by a detailed numerical example where we study a right one-sided fuzzy test and compare it with a classical one. We close the paper by an application of the method on a survey from the financial place of Zurich, Switzerland. We display the decisions related to tests on the mean made on a set of variables of the sample. Both fuzzy and classical tests are conducted. One of our main findings is that despite the fact that each of both approaches have a different decision rule in terms of interpretation, the decisions made are by far the same. In this perspective, we can state that the fuzzy testing procedure can be seen as a generalization of the classical one.

Lab head

Laurent Donzé
Department
  • Department of Informatics

Members (6)

Rédina Berkachy
  • Université de Fribourg
Martina Raggi
  • French Institute of Health and Medical Research
Layal Christine Lettry
  • Université de Fribourg
A. Turková
  • Université de Fribourg
Thu-Hang Nguyen
  • Université de Fribourg