## One-sample tests for a generalized Fréchet variance of a fuzzy random variable.(English)Zbl 1182.62103

Summary: A procedure to test hypotheses about the population variance of a fuzzy random variable is analyzed. The procedure is based on the theory of UH-statistics [see W. Hoeffding, Ann. Math. Stat. 19, 293–325 (1948; Zbl 0032.04101)]. The variance is defined in terms of a general metric to quantify the variability of the fuzzy values about its (fuzzy) mean. An asymptotic one-sample test in a wide setting is developed and a bootstrap test, which is more suitable for small and moderate sample sizes, is also studied. Moreover, the power function of the asymptotic procedure through local alternatives is analyzed. Some simulations showing the empirical behavior and consistency of both tests are carried out. Finally, some illustrative examples of the practical application of the proposed tests are presented.

### MSC:

 62G10 Nonparametric hypothesis testing 62G20 Asymptotic properties of nonparametric inference 62G09 Nonparametric statistical resampling methods 62G86 Nonparametric inference and fuzziness 65C60 Computational problems in statistics (MSC2010)

Zbl 0032.04101
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