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Title: Estimating the wrapped stable distribution via indirect inference Authors:  Marco Bee - University of Trento (Italy) [presenting]
Abstract: Directional data are frequently encountered in applications and require a special treatment. One way of constructing probability distributions for directional data exploits the idea of wrapping on the unit circle a distribution defined on the real line. We study estimation of the wrapped stable distribution, and propose a novel approach based on constrained indirect inference. Since the wrapped stable density does not exist in closed-form, simulation-based methods are an appealing alternative to maximum likelihood. The problem is tackled by means of a strategy already used for indirect inference estimation of the linear stable distribution. In particular, we use the wrapped version of the same auxiliary model, namely the skewed-$t$ distribution. We study numerically the impact of the inputs, and especially of the weighting matrix, in finite samples. Simulation experiments suggest that indirect inference is more efficient than numerical maximum likelihood, from both the statistical and the computational point of view.