A method for estimating the parameters of the Rasch model is examined. The unknown quantities in this method are the item parameters and the distribution function of the latent trait over the population. In this sense, the method is equivalent to marginal maximum likelihood estimation. The new procedure is based on a method suggested by J. Kiefer and J. Wolfowitz (1956). Their conclusions are reviewed, and links to the Rasch model are specified. In marginal maximum likelihood estimation, the item parameters are estimated first, and then the prior distribution of the person parameters is estimated using these estimates. The proposed method illustrates that it is possible to estimate these two quantities together and arrive at consistent estimates. Two data tables are provided. (SLD)