Choosing the smoothing parameter for unordered multinomial data

We consider the estimation of multinomial probabilities in the non-sparse univariate unordered case. We describe a number of explicit methods (mostly pre-existing) for the choice of the smoothing parameter in this context. In simulations, we compare these methods in terms of mean root mean squared error performance. Our recommendation is for the routine use of the simplest Bayesian estimation formula in which the probability in thek'th cell is estimated by (n _k +1)/(N+K) wheren _k is the count in thek'th cell,N is the sample size andK is the number of cells.