Estimation and Inference of Skew–Stable distributions using the Multivariate Method of Simulated Quantiles

The multivariate method of simulated quantiles (MMSQ) is proposed as a likelihood–free alternative to indirect inference procedures that does not rely on an auxiliary model specification and its asymptotic properties are established. As a further improvement we introduce the Smoothly clipped absolute deviation (SCAD1 –penalty into the MMSQ objective function in order to achieve sparse estimation of the scaling matrix.We extend the asymptotic theory and we show that the sparse– MMSQ estimator enjoys the oracle properties under mild regularity conditions. The method is applied to estimate the parameters of the Skew Elliptical Stable distribution