## Preprint 2016-16

## Luis M. Castro, José González, Víctor H. Lachos, Alexandre Patriota:

### A confidence set analysis for observed samples: A fuzzy set approach

### Abstract:

Condence 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 condence sets have probability zero or one to contain the parameter value. In this paper, we provide a condence 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 condence and signicance 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.

This preprint gave rise to the following definitive publication(s):

**Luis M. CASTRO, José GONZáLEZ, Víctor H. LACHOS, Alexandre PATRIOTA: ***A confidence set analysis for observed samples: A fuzzy set approach*. Entropy, vol. 18, 211, pp. 1-22, (2016).