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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 (SCAD) $\ell_1$--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.