A new multinomial model and a zero variance estimation

The analysis of categorical response data through the multinomial model is very frequent in many statistical, econometric, and biometric applications. However, one of the main problems is the precise estimation of the model parameters when the number of observations is very low. We propose a new Bayesian estimation approach where the prior distribution is constructed through the transformation of the multivariate beta of Olkin and Liu (2003). Moreover, the application of the zero-variance principle allows us to estimate moments in Monte Carlo simulations with a dramatic reduction of their variances. We show the advantages of our approach through applications to some toy examples, where we get efficient parameter estimates.