## A new way of quantifying the symmetry of a random variable: estimation and hypothesis testing.(English)Zbl 1348.62161

Summary: New measures of skewness for real-valued random variables are proposed. The measures are based on a functional representation of real-valued random variables. Specifically, the expected value of the transformed random variable can be used to characterize the distribution of the original variable. Firstly, estimators of the proposed skewness measures are analyzed. Secondly, asymptotic tests for symmetry are developed. The tests are consistent for both discrete and continuous distributions. Bootstrap versions improving the empirical results for moderated and small samples are provided. Some simulations illustrate the performance of the tests in comparison to other methods. The results show that our procedures are competitive and have some practical advantages.

### MSC:

 62G10 Nonparametric hypothesis testing 62E20 Asymptotic distribution theory in statistics 62G09 Nonparametric statistical resampling methods 62G20 Asymptotic properties of nonparametric inference 62G86 Nonparametric inference and fuzziness
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### References:

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