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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

A Confidence Set Analysis for Observed Samples: A Fuzzy Set Approach

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Alejandro Gonzalez, Jose [1] ; Mauricio Castro, Luis [2, 3] ; Lachos, Victor Hugo [4] ; Patriota, Alexandre Galvao [5]
Total Authors: 4
[1] Univ Playa Ancha, Dept Matemat & Estadist, Valparaiso 2340000 - Chile
[2] Univ Concepcion, Dept Estadist, Concepcion 4030000 - Chile
[3] Univ Concepcion, CI2MA, Concepcion 4030000 - Chile
[4] Univ Estadual Campinas, Dept Estat, BR-13083859 Campinas, SP - Brazil
[5] Univ Sao Paulo, Dept Estat, IME, BR-05508090 Sao Paulo - Brazil
Total Affiliations: 5
Document type: Review article
Source: Entropy; v. 18, n. 6 JUN 2016.
Web of Science Citations: 3

Confidence sets are generally interpreted in terms of replications of an experiment. However, this interpretation is only valid before observing the sample. After observing the sample, any confidence sets have probability zero or one to contain the parameter value. In this paper, we provide a confidence set analysis for an observed sample based on fuzzy set theory by using the concept of membership functions. We show that the traditional ad hoc thresholds (the confidence and significance levels) can be attained from a general membership function. The applicability of the newly proposed theory is demonstrated by using well-known examples from the statistical literature and an application in the context of contingency tables. (AU)

FAPESP's process: 11/17400-6 - Applications of the scale mixture of Skew-Normal distributions in linear mixed effects models
Grantee:Víctor Hugo Lachos Dávila
Support type: Regular Research Grants
FAPESP's process: 12/19445-0 - Flexible modeling of complex longitudinal data using skew-elliptical distributions
Grantee:Víctor Hugo Lachos Dávila
Support type: Research Grants - Visiting Researcher Grant - International
FAPESP's process: 14/25595-0 - Comparisons between the s-value and some classical measures of evidences
Grantee:Alexandre Galvão Patriota
Support type: Scholarships abroad - Research