Abstract
The standard root-b1 test is widely used for testing skewness. However, several studies have demonstrated that this test is not reliable for discriminating between symmetric and asymmetric distributions in the presence of excess kurtosis. The main reason for the failure of the standard root-b1 test is that its variance formula is derived under the assumption of no excess kurtosis. In this paper we theoretically derive adjustment to the root-b1 test under the framework of Roa's Score (or the Lagrange multiplier) test principle. Our adjusted test automatically corrects the variance formula and does not lead to over- or under-rejection of the correct null hypothesis. In a similar way, we also suggest an adjusted test for kurtosis in the presence of asymmetry. These tests are then applied to both simulated and real data. The finite sample performances of the adjusted tests are far superior compared to those of their unadjusted counterparts.
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