Abstract
We consider risk-efficient sequential estimation under squared error loss of the number of classes which are equally probable to occur in a given multinomial population. It is assumed that the sampling cost per observation is constant. Large-sample properties of the sequential estimator are studied. Finally, Monte Carlo simulation is carried out in order to investigate its finite sample behavior. The proposed sequential procedure performs better (in the sense of reducing average stopping time and risk) than the one based on the estimator K n , the number of distinct cells observed in a sample of size n.