Estimating the wrapped stable distribution via indirect inference

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We develop a constrained indirect inference approach based on a wrapped skewed-t auxiliary model for the estimation of the wrapped stable distribution. To improve the finite-sample properties of the estimators, we devise a bootstrap-based estimate of the weighting matrix employed in the indirect inference program. The simulation study suggests that, in terms of root-mean-squared-error, the indirect inference estimator of the skewness parameter is slightly better than the corresponding maximum likelihood estimator, whereas maximum likelihood is mostly preferable for the other parameters. In terms of computing time, maximum likelihood is faster.