Iterative weighted LAD estimation with homoskedasticity testing using the Gini concentration index

An iterative technique is presented for weighted least absolute deviation (LAD) estimation, incorporating weights derived from the sparsity function associated with the response variable. The initial condition assumes homoskedastic residuals. The method’s essence lies in interpolating the unconditioned quantile function of the responses within a narrow neighborhood around 0.5. This interpolation yields an approximation of the sparsity function, which, in turn, guides the updating of weights based on the reciprocals of sparsity function values. These iterative steps are repeated until a predefined stopping criterion is satisfied. We propose using the Gini concentration index of these weights to assess the presence of heteroskedasticity in LAD residuals. The test statistic follows an asymptotic standard Gaussian distribution under the null hypothesis. We provide a simulation study to demonstrate the application and finite-sample performance of this test. Our results provide evidence for the utility of the Gini test.