Likelihood inference for the Bingham distribution is dicult because the density function contains a normalization constant that cannot be computed in closed form. We propose to estimate the parameters by means of Approximate Maximum Likelihood Estimation (AMLE), thus bypassing the problem of evaluating the likelihood function. We study the impact of the input parameters of the AMLE algorithm and suggest some methods for choosing their numerical values. Moreover, we compare AMLE to the standard approach consisting in maximizing numerically the (approximate) likelihood obtained with the normalization constant estimated via the Holonomic Gradient Method (HGM). For the Bingham distribution on the sphere, simulation experiments and real-data applications produce similar outcomes for both methods. On the other hand, AMLE outperforms HGM when the dimension increases.

Keywords: Directional data; Simulation; Intractable Likelihood; Sucient statistics