Conference Paper

# Fuzzy Confidence Intervals by the Likelihood Ratio with Bootstrapped Distribution

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... Detailed examples illustrating this definition can be found in Berkachy [2] and Berkachy and Donzé [7]. ...
... We presented in Berkachy and Donzé [7] and Berkachy and Donzé [5] a generalisation of the traditional construction procedure. The aim was to show a practical tool based on the concept of likelihood ratio method to estimate fuzzy confidence intervals, in which the fuzziness contained in the variables is conveniently taken into consideration. ...
... In this section, we briefly recall the defended procedure. Note that further detailed information can be found in Berkachy and Donzé [7] and Berkachy [2]. ...
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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.
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