Estimating a Rasch Model via fuzzy empirical probability functions

The joint maximum likelihood estimation of the parameters of the Rasch model is hampered by several drawbacks, the most relevant of which are that: i) the
estimates are not available for item or person with perfect scores; ii) the item parameter estimates are severely biased, especially for short tests. To overcome both these
problems, in this paper a new method is proposed, based on a fuzzy extension of the empirical probability function and the minimum Kullback-Leibler divergence
estimation approach. The new method warrants the existence of finite estimates for both person and item parameters and results very effective in reducing the bias of joint
maximum likelihood estimates.