The logarithmic super divergence and asymptotic inference properties

Statistical inference based on divergence measures have a long history. Recently, Maji et al. (The logarithmic super divergence and its use in statistical inference, Bayesian and Interdisciplinary Research Unit, Indian Statistical Institute, India, 2014a) have introduced a general family of divergences called the logarithmic super divergence family. This family acts as a superfamily for both the logarithmic power divergence family (eg., Renyi, Proceedings of 4th Berkeley symposium on mathematical statistics and probability, vol. I, pp. 547-561, 1961) and the logarithmic density power divergence family introduced by Jones et al. (Biometrika 88:865-873, 2001). In this paper, we describe the asymptotic properties of the inference procedures based on these divergences in discrete models. The performance of the method is demonstrated through real data examples.