Entropy 2016, 18(6), 211; https://doi.org/10.3390/e18060211
A Confidence Set Analysis for Observed Samples: A Fuzzy Set Approach
José Alejandro González 1, Luis Mauricio Castro 2, Víctor Hugo Lachos 3 and Alexandre Galvão Patriota 4,*
1
Departamento de Matemática y Estadística, Universidad de Playa Ancha, Valparaíso 2340000, Chile
2
Departamento de Estadística and CI2MA, Universidad de Concepción, Concepción 4030000, Chile
3
Departamento de Estatística, Universidade Estadual de Campinas, Campinas 13083-859, Brazil
4
Departamento de Estatística, IME, Universidade de São Paulo, São Paulo 05508-090, Brazil
*
Author to whom correspondence should be addressed.
Academic Editors: Julio Stern, Adriano Polpo and Antonio M. Scarfone
Received: 20 March 2016 / Revised: 13 May 2016 / Accepted: 25 May 2016 / Published: 30 May 2016
(This article belongs to the Special Issue Statistical Significance and the Logic of Hypothesis Testing)
Abstract
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. View Full-TextKeywords:
confidence sets; fuzzy sets; membership function; possibility theory
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González, J.A.; Castro, L.M.; Lachos, V.H.; Patriota, A.G. A Confidence Set Analysis for Observed Samples: A Fuzzy Set Approach. Entropy 2016, 18, 211.
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