Abstract:

In many practical applications, data about an unknown continuous distribution arise in a grouped form. For these cases, estimation of population entropies and divergences must be done by means of their sample discretized estimates. In this paper, the problem of loss of information due to the discretization of the data is studied for $(h,\phi)$-entropies and $R^{h}_{\phi}$-divergences. Quadratic convergence theorems are given and asymptotic distributions are obtained.