The likelihood ratio test to test for symmetry, in the context of a framework of quantile-based asymmetric family of densities is discussed in Gijbels et al. (2019d).
This is a vector of quantiles.
This is the reference density function f which is a standard version of a unimodal and symmetric around 0 density.
The likelihood ratio test statistic with P-value.
Gijbels, I., Karim, R. and Verhasselt, A. (2019d). Test of symmetry and a quantile-based asymmetric family of densities, Manuscript.
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